Only the person(s) on the Mortgage Loan can claim the Mortgage Interest, as they are the only person(s) responsible for the payment of the loan.
From IRS Publication 936:
"In Publication 936, the IRS states that you can deduct mortgage interest if you itemize deductions on Schedule A and are “legally liable” for the loan. The IRS also says that you cannot deduct payments you make for someone else if you are not legally liable to make them."