No, the student is legally obligated to make the payments, therefore, only the student may take the deduction [Reg. §1.221-1(b)].

Generally, you can claim a deduction for student loan interest if all of the following are met.
1. Your filing status is not MFS.
2. No one else is claiming your exemption.
3. You are legally obligated to pay the interest.
4. You paid the interest. 

An exception to item #4 would be if a parent or grandparent made the student loan payment as a "gift" for the student. Then the student would still be able to claim the student loan deduction.
Again, only the party legally responsible to make the payments is entitled to the deduction.