Note: As a broad generality, schools in higher clusters are more likely to offer "no co-signer" loans than schools in lower clusters. As usual, it is important to study the specific requirements of each school with care.
Corrections and/or additions are welcome!
Chicago
"Student Loans for International Students
Chicago GSB has two private, credit-based alternative loan programs available for international students. One loan program requires a creditworthy co-signer who is a U.S. Citizen or U.S. Permanent Resident currently living in the United States. The other loan program does not require a co-signer. Students borrowing from either loan program can borrow up to the budget amount less any scholarships or other financial assistance received."
https://gsb.uchicago.edu/fulltime/admiss ... alaid.aspx
Harvard
"available to all HBS Students regardless of citizenship"
https://www.hbs.edu/mba/admissions/loanprograms.html
MIT "No co-signer is required."
https://mitsloan.mit.edu/mba/admissions/loans.php
Penn (Wharton)
"Wharton also provides access to the Wharton International Loan Program offered through Citibank. Eligibility is guaranteed with 100% of students approved for borrowing."
https://mba.wharton.upenn.edu/mba/admiss ... /loans.php
Dartmouth (Tuck)
Tuck School of Business International loans
"Unique loan program for international students
Students may be eligible to borrow up to full tuition and fees (as determined by the Financial Aid Office)
Does not require a U.S. guarantor or co-borrower"
https://www.tuck.dartmouth.edu/admissions/aid/loans.html
Duke (Fuqua) No co-signor required
https://www.fuqua.duke.edu/admin/stuserv ... tional.htm
Michigan No Co-signer required
"No Co-signer is required for domestic or international students"
https://www.bus.umich.edu/Admissions/Mba ... stLoan.htm
UNC The North Carolina EXTRA MBA Loan
https://www.kenan-flagler.unc.edu/Progra ... on/aid.cfm
Indiana No co-signor loan option for all admitted intl. students
https://www.kelley.iu.edu/MBA/admissions/finaid.cfm