Can I list tuition expenses for grad school if they're paid on my behalf by my school using internal grants?

-Yes, if the school is an eligible education institution, you can enter the amounts using your student account statement. You also need to report the grants. 

Some schools do not issue a 1098-T if the tuition was covered by scholarships and/or grants, but you might still be eligible for a deduction or credit if you can allocate some of the aid to other education expenses, such as room and board. 

Be sure to only use expenses paid in 2020 for classes attended in 2020 and/or the first three months of 2021. 

IRS Pub 970 

Q.  Can I list tuition expenses for grad school if they're paid on my behalf by my school using internal grants?

A. No.  You may NOT use expenses, paid by tax free grants, to claim a tuition credit or deduction.

But, there may be a loop hole available.    The student reports all his scholarship, up to the amount needed to claim a tuition credit, as income on his return. That way, the parents  (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship.  You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.

Using an example: Student has $12,000 in box 5 of the 1098-T and $10,000 in box 1. At first glance he/she has $2000 of taxable income and nobody can claim the tuition credit. But if she reports $12000 as income on her return, the parents can claim $10,000 of qualified expenses on their return (for grad students, it takes $10K of expenses to get the maximum $2000 Lifetime Learning credit). 

This is the same technique KrisD15 described  when he suggested  "allocate some of the aid to other ("non qualified") education expenses, such as room and board".