Assuming an Apollo-style mission (two-stage lander, with return vessel holding in orbit for return), this mission would just about be possible, physically, with today's rockets.
Humanly, it's not possible at all. Mercury is the hardest place in the Solar System to reach, saving only the Sun itself, in terms of the universal currency of space travel, Delta-V. You have to nearly kill Earth's orbital velocity to fall down that close to the sun, then you have to almost match velocity with Mercury to make orbit there (and without any ability to aerobrake as is often done with Mars). Your lander will be heavier, as it takes much more rocket power to reach orbit from Mercury than from our Moon -- and the descent stage has to carry that larger ascent vehicle to a safe landing on rockets only. You might wind up with a lander resembling the SpaceX Starship and Starbooster just for your lander.
And at the end, you need to have enough propellants still in the transfer vehicle to return to at least an aerobrake at Earth. The mission will take a minimum of several months, and the launch mass would be equivalent to at least four or five Saturn V launches.
Alternatively, to get a mission you could launch on a Delta IV Heavy or Falcon Heavy, the return vehicle would be too small to carry even a single human, and even then you'd have to use multiple gravity assists from Earth and Venus (and probably at least one from Mercury) to substitute for lack of fuel -- and the mission would consume years each way, instead of months. The major objection to sending humans to Mars is trip time -- with a multiple gravity assist trip to Mercury, the trip time would be several times longer.
Bottom line, nuclear propulsion (either a nuclear-thermal rocket of some kind or an Orion style pulse drive) would be the only way to send the necessary lander there and bring the crew back in a reasonable time frame.