Your best bet is probably Sichuan University or the Minorities University in Chengdu. If you go to either of those places and inquire you can get all the information you need.
Unfortunately I don’t know of any small private places to learn Chinese in that kind of academic environment without signing up at University. If there were a private school that’s catered to the needs of its students and didn’t require so much commitment, that would be a great option. Otherwise, there’s always self-study. Good luck-