SHORT ANSWER:
Nobody knows for certain, but some calculations indicate that it would be possible for a gas giant planet to have least two and possibly as many as four large and potentially habitable moons orbiting within the proper distance from the planet.
My long answer below my original answer, added on May 8, 2020, goes into some detail about the question.
You should use the search function at the top of the page and search for other questions about habitable moons of giant planets.
I have answered a number of those questions myself.
Among the useful sources are:
Stephen H. Dole, in Habitable Habitable Planets for Man (1964,2007)
https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf1
Heller, René; Rory Barnes (2012). "Exomoon habitability constrained by illumination and tidal heating". Astrobiology. 13 (1): 18–46.
https://arxiv.org/ftp/arxiv/papers/1209/1209.5323.pdf2
And:
Heller, René (September 2013). "Magnetic shielding of exomoons beyond the circumplanetary habitable edge". The Astrophysical Journal Letters. 776 (2): L33.
https://arxiv.org/pdf/1309.0811.pdf3
I wrote a long answer to this question:
What types of flora would flourish on a tidally-locked moon?2
There I discuss some of the various limits of hypothetical habitable exomoons of exoplanets.
LONG ANSWER added on May 8, 2020:
At the PlanetPlanet blog the section Ultimate Solar system has posts about designing fictional solar systems with as many habitable worlds as possible.
The Building the Ultimate Solar System series explains how I would go about building a new Solar System. My goal is to maximize the number of potentially life-bearing worlds in a single system. I take a bottom-up approach. I first discuss the pieces involved — stars, planets, orbits — then put them all together. Then I take things farther, and then way way too far…
https://planetplanet.net/the-ultimate-solar-system/5
Those fictional solar systems sometimes include solar systems with giant planets in the habitable zone and Earth sized habitable moons orbiting those planets.
He discusses how many large, habitable moons a gas giant planet could have:
e biggest Solar System moons orbit the biggest planets (Jupiter and Saturn). Systems of moons form like mini-Solar Systems, in disks of gas and dust around gas giant planets. [In fact, large Solar System moons have some properties in common with extra-solar planets]. The moons are located very close to the gas giants. The orbits of the most distant large moons are only about 30 times larger than the radius of their host planet. In comparison, Earth’s orbit is about 200 times larger than the radius of the Sun.
We want worlds in our ultimate Solar System that are a little bigger than these large moons. We want worlds about half to twice Earth’s size. Although there is some debate, I’m going to allow any gas giant that is Saturn-sized or larger to have large moons.
In the Solar System, Jupiter has the most (four). Given how close-in the Solar System moons are located, large moons are likely to stay close. But how many big moons could a gas giant have? Well, at least as many as Jupiter (four). But probably not that many more. The orbits of planets and moons tend to be spaced logarithmically. Think, 1, 10, 100, 1000 rather than 10, 20, 30, 40. The farther from the star/planet, the bigger the spaces between planets/moons. If the zone with large moons extends from 5 to 50 times the planet’s radius, this only gives us room for 5 large moons spaced like Jupiter’s. We’ll stick with a maximum of 5 large moons per gas giant planet.
https://planetplanet.net/2014/05/22/building-the-ultimate-solar-system-part-4-two-ninja-moves-moons-and-co-orbital-planets/6
So he thinks that it is possible for a giant planet to have as many as 5 large moons with about 0.5 to 2.0 times Earth's mass.
But he does have a link to "some debate" about massive moons, an article calculating that Moon to Mars mass satellites would be the most massive likely to form around giant planets, which would not be massive enough for habitability.
https://ui.adsabs.harvard.edu/abs/2006Natur.441..834C/abstract7
I note that the giant planets in our solar system have the following masses: Jupiter 317.8 Earth mass, Saturn 95.2 Earth mass, Uranus 14.6 Earth mass, and Neptune 17.2 Earth mass.
Ganymede, the most massive moon of Jupiter has a mass of 0.0248 Earth mass or 0.000078 Jupiter's mass; Titan, the most massive moon of Saturn has a mass of 0.0225 Earth mass or 0.0002363 of Saturn's mass; Titania, he most massive moon of Uranus has a mass of 0.00059 Earth mass or 0.0000404 Uranus's mass; Triton, the most massive moon of Neptune has a mass of 0.003599 Earth's mass or 0.0002092 of Neptune's mass.
I note that the Moon has 0.0123 the mass of it's planet, Earth, and Charon, the largest moon of the dwarf planet Pluto, has a mass of 0.1218 Pluto's mass. The Moon is believed to have been formed when a small planet collided with Earth billions of years ago, and Pluto and Charon may have captured each other, while Triton is believed to have been captured by Neptune.
Since no exomoons have been discovered in other star systems yet, Titan is believed to be the normally forming moon with the most mass relative to its giant planet primary with a mass 0.0002363 of Saturn's mass, or 0.2363 percent.
Jupiter has four large moons, with masses of 0.015 Earth or of 0.0000471 Jupiter (Io), 0.008035 of Earth or 0.0000252 of Jupiter (Europa), 0.0248 of Earth or 0.000078 of Jupiter (Ganymede), and 0.018 of Earth or 0.0000566 of Jupiter (Callisto).
So among moons that formed normally in circumplanetary discs, Jupiter has four moons that each have at least 0.0000252 of its mass, including two that each have at least 0.0000566 of its mass, while Saturn has one moon with 0.0002363 of it's mass.
Planet's can get much more massive than Jupiter, although they will not normally get much larger than Jupiter, since more massive planets will be compressed more by their gravity and become more dense than Jupiter.
The most massive planets would be about 13 times as massive as Jupiter, or about 4,131.4 times as massive as Earth. More massive objects would be brown dwarfs, up to about 75 to 80 times the mass of Jupiter, or about 23,835 to times the mass of Earth.
Using the examples in our solar system as a limit, the most massive possible planet, at about 13 Jupiter masses or 4,131.4 Earth masses, could have four moons each at least 0.0000252 of its mass or 0.1041 Earth's mass, or two moons each having at at least 0.0000566 of its mass or 0.2338 Earth's mass, or one moon with 0.0002363 of its mass or 0.9762 of Earth's mass.
Using the examples in our solar system as a limit, the most massive possible brown dwarf, with 75 to 80 Jupiter masses or 23,835 to 25,424 Earth masses, could have four satellites that each have at least 0.0000252 of its mass, or 0.6006 to 0.6406 Earth's mass, and/or two that each have at least 0.0000566 of its mass, or 1.3490 to 1.4389 Earth's mass, and/or one satellite with 0.0002363 of its mass, or 5.6322 to 6.0076 Earth's mass.
So using the known mass ratios of giant planets to moons in our solar system as a guide, a would would have to be the most massive possible planet or a brown dwarf to have moons near the mass of Earth that formed in the circumplanetary disc of that planet.
Of course it is possible that even Titan does not have the largest possible mass ratio of a moon forming in the planetary disc to its giant planet primary. to his
One of the sources I listed above:
Heller, René; Rory Barnes (2012). "Exomoon habitability constrained by illumination and tidal heating". Astrobiology. 13 (1): 18–46.
https://arxiv.org/ftp/arxiv/papers/1209/1209.5323.pdf2
does discuss whether giant exoplanets could have exomoons massive enough to be habitable in section 2.1, Formation of massive satellites.
The largest and most massive moon in the Solar System, Ganymede, has a radius of only ≈0.4R⊕ (R⊕ being the radius of
Earth) and a mass of ≈0.025M⊕. The question as to whether much more massive moons could have formed around
extrasolar planets is an active area of research. Canup & Ward (2006) have shown that moons formed in the circumplanetary disk of giant planets have masses ≲10-4 times that of the planet’s mass. Assuming satellites formed around
Kepler-22b, their masses will thus be 2.5×10-3M⊕ at most, and around KOI211.01 they will still weigh less than Earth’s
Moon. Mass-constrained in situ formation becomes critical for exomoons around planets in the IHZ of low-mass stars
because of the observational lack of such giant planets. An excellent study on the formation of the Jupiter and the Saturn
satellite systems is given by Sasaki et al. (2010), who showed that moons of sizes similar to Io, Europa, Ganymede, Callisto,
and Titan should build up around most gas giants. What is more, according to their Fig. 5 and private communication with
Takanori Sasaki, formation of Mars- or even Earth-mass moons around giant planets is possible. Depending on whether or
not a planet accretes enough mass to open up a gap in the protostellar disk, these satellite systems will likely be multiple and
resonant (as in the case of Jupiter), or contain only one major moon (see Saturn). Ogihara & Ida (2012) extended these
studies to explain the compositional gradient of the jovian satellites. Their results explain why moons rich in water are
farther away from their giant host planet and imply that capture in 2:1 orbital resonances should be common.
Ways to circumvent the impasse of insufficient satellite mass are the gravitational capture of massive moons (Debes &
Sigurdsson 2007; Porter & Grundy 2011; Quarles et al. 2012), which seems to have worked for Triton around Neptune
(Goldreich et al. 1989; Agnor & Hamilton 2006); the capture of Trojans (Eberle et al. 2011); gas drag in primordial circumplanetary envelopes (Pollack et al. 1979); pull-down capture trapping temporary satellites or bodies near the Lagrangian
points into stable orbits (Heppenheimer & Porco 1977; Jewitt & Haghighipour 2007); the coalescence of moons (Mosqueira
& Estrada 2003); and impacts on terrestrial planets (Canup 2004; Withers & Barnes 2010; Elser et al. 2011). Such moons
would correspond to the irregular satellites in the Solar System, as opposed to regular satellites that form in situ. Irregular
satellites often follow distant, inclined, and often eccentric or even retrograde orbits about their planet (Carruba et al. 2002).
For now, we assume that Earth-mass extrasolar moons – be they regular or irregular – exist.
So in 2012 there were several theoretically studies indicating that giant planets could form or acquire natural satellites more massive than merely Moon sized, possibly even Earth sized or much larger.
Going back to the PlanetPlanet discussion of large, roughly Earth mass exomoons orbiting gas giant exoplanets, he says:
If the zone with large moons extends from 5 to 50 times the planet’s radius, this only gives us room for 5 large moons spaced like Jupiter’s. We’ll stick with a maximum of 5 large moons per gas giant planet.
But one of the sources I listed above:
Heller, René (September 2013). "Magnetic shielding of exomoons beyond the circumplanetary habitable edge". The Astrophysical Journal Letters. 776 (2): L33.
https://arxiv.org/pdf/1309.0811.pdf3
Discusses what could be called the circumplanetary habitable zone, where hypothetical giant exomoons would be orbiting at the proper distance from the planet to be protected from charged particles by the planetary magnetic field.
Heller concludes that giant exomoons could be habitable if they orbit within a range of 5 to 20 planetary radii from the planet. That is a much narrower range than 5 to 50 planetary radii from the planet, only a third as wide.
Neptune has an equatorial radius of about 24,760 kilometers, so it would have a circumplanetary habitable zone between about 123,800 to 495,500 kilometers. Only one moon, the large Triton, orbits within that zone.
Uranus has an equatorial radius of about 25,560 kilometers, so it would have a circumplanetary habitable zone between about 127,800 to 511,200 kilometers. It has four moons, Miranda, Ariel, Umbriel, and Titania, in four separate orbits within that zone.
Saturn has an equatorial radius of about 60,268 Kilometers, so it would have a circumplanetary habitable zone between about 301,340 to 1,205,360 kilometers. Saturn has four moons within that zone, Dione, Helene, Polydeuces, and Rhea, but in only two obits, since Helene and Polydeuces are in Trojan orbits relative to Dione.
Jupiter has an equatorial radius of about 71,492 Kilometers, so it would have a circumplanetary habitable zone between about 357,460 to 1,429,840 kilometers. Jupiter has three moons, Io, Europa, and Ganymede, orbiting within that zone.
Thus, if Heller's calculations are correct, the giant planets in our solar system have one, two, three, and four satellite orbits within their respective circumplanetary habitable zones. Thus it does seem plausible for a Saturn sized planet to have two large and potentially habitable moons orbiting within its circumplanetary habitable zone.
