Asteroids are unpromising - in fact abyssmal - terrain for mining rare earth elements. They exist in very low concentration - as we know from meteorites - and there are probably no rare earth ores on any of them.
Rare earth elements are strongly lithophile, therefore they accumulate in planetary crusts. Earth may be the best place in the solar system for mining REEs, because we have a high bulk abundance of them and geological processes that led to the formation of ores. And we have a strong gravity which enables placer deposits (where most REEs are mined from monazite sand).
Mars seems to have a somewhat lower bulk abundance of REEs than Earth, except for scandium which is more abundant.
On asteroids bulk abundance of light REEs is typically 100 times lower than in the Earth crust and 20-30 times lower for heavy REEs.
Elevated concentrations of REEs are found in phosphate minerals like whitlockite, but still much lower than in average rocks on Earth.
As far as I know there is only one mineral on asteroids that has a higher concentration of REEs than terrestrial rocks, and that is OLDHAMITE, a calcium sulfide mineral which is extremely rare on Earth but common in a certain class of meteorites: metal-rich ENSTATITE CHONDRITES and rocky ENSTATITE ACHONDRITES.
Oldhamite seems to "suck" all the REEs from the rest of the meteorite and can host 10 to 1000 times more REEs than the matrix. Due to extremely low bulk abundance that is still not enough that it would count as REE ore on Earth, but it already comes close, especially for heavy rare earth elements because we have no good ores for them either. Oldhamite is enriched in heavy REEs compared to light REEs. That is because of the refractory nature of HREEs (Oldhamite forms at high temperature).
It is possible that you find oldhamite on asteroids which is even more enriched in REEs than the ones we know from meteorites. That would count as REE ore, at least for HREEs (which are also the expensive ones anyway).
Unfortunately, the lower the abundance of oldhamite in a meteorite, the more enriched it is in REEs. That is the opposite of what we want. Oldhamite with an enrichment factor of 1000 never constitutes more than fractions of a % in an enstatite meteorite. On the other hand, when oldhamite is abundant it is relatively poor in REEs.
So to find an asteroid that can be mined for REEs it would not only have oldhamite that is unusually rich in REEs, there would also have to be a secondary enrichment of oldhamite. That may happen, because oldhamite has a higher melting point than surrounding rocks, but lower density, so it would float in a melt. I would search for it on a large, massive asteroid where igneous processes took place in the past so that separation of rare earth elements from the bulk and separation of odhamite from the rest of the melt phase could occur. Also, oldhamite needs reducing conditions to form, it does not occur when oxygen abundance is too high. All oldhamite containing meteorites probably formed close to the sun (it is expected to be a common mineral on Mercury).
According to spectral analysis some asteroids may contain large amounts of odhamite on the surface (up to 10%).
But, as I mentioned at the beginning, there is probably nothing in the solar system as good for mining REEs as our placer deposits.Long story short, the answer of your question is "no", but it gave me the rare opportunity to talk about one of my favorite minerals.