No, paying off a debt for college expenses incurred in previous years is not a deductible expense.
However, you may be able to deduct student loan interest up to $2,500 on a qualified student loan
Per the IRS, "a qualified student loan is a loan that was taken out solely to pay qualified education expense that were for the taxpayer, spouse, or a person who was a dependent (defined earlier in this course) when the loan was taken out.
The loan must be paid or incurred within a reasonable period of time before or after the loan was taken out, and for education provided during an academic period for an eligible student.
Loans from a related person or a qualified employer plan are not qualified student loans."
You must also be legally obligated to pay the interest.