Sen. John Cornyn, the No. 2 Senate Republican, signaled Thursday that the GOP could tweak its treatment of popular tax deductions in its final tax bill.

The separate bills passed by the House and Senate scrap most state and local deductions but leave up to $10,000 in property tax deductions in place. As the chambers move to strike a joint plan in a conference committee, some House members in high-tax blue states have pushed for a state and local income tax deduction, as well.

Cornyn, a Texas Republican, suggested Thursday that more changes to those tax breaks could come.

"I talked to [House Majority Leader Kevin] McCarthy the other night, and he did tell me that this is an item of contention in the House," the Senate majority whip told CNBC's "Squawk Box." "I don't know what's going to happen to that. We did adopt the $10,000 deduction for property taxes but there may be some movement in that space. I, frankly, would anticipate that."