I checked three schools.
Brown University states that transfer students who apply for need based financial aid will be reviewed “need aware”, not “need blind”, for transfer applicants.
Vanderbilt University just notes that international transfer applicants seeking financial aid will not be offered admission.
Over the years, I have seen financial aid policies from various schools place qualified transfer applicants in need of financial aid on the wait-list if budgeted financial aid funds have been exhausted, while other schools place transfer applicants at the back of the line for financial aid so that if aid is depleted, then transfer students may be admitted but not offered financial aid.
I hesitate to name schools as policies change for both institutional and sometimes for governmental reasons.
If in need of financial aid as a domestic transfer student, then apply as all schools seem to indicate that transfer students are eligible to apply for financial aid. Whether that means review under a need-aware basis or a back-of-the-line approach or both should be examined on an institution by institution basis.