No. That is, you can ask, but they will refuse to answer, so it's better not to bother.
Private universities do not reserve places for transfer students, so vacancies are dependent on how many students drop out. They could have very few spots and a large number of applicants.
Public universities do reserve places for transfer students, but only for those who are transferring in from transfer-agreement community colleges. These students have preference, and transfers from other in-state colleges and universities have second preference, so non-internal transfers are typically admitted only if every qualified preferred candidate is placed.
If a university is competitive, just because you are well-qualified does not mean you are automatically admitted. It might have five or more very qualified applicants for each vacancy. Unless your application stands out in some way -- not a silly way, but through your academic achievements -- you will probably be overlooked.
So, consider it a "win" that you were interviewed by the competitive university -- they were actually considering you (yay!); they didn't immediately throw your application into the bin -- and chalk it up to a life experience that you can't always get what you want.