The expectation that a debt deal may be forthcoming from talks between Senate Majority Leader Harry Reid and Republican leader Mitch McConnell is "very possible," Sen. Bob Corker, R-Tenn., told CNBC on Monday.

"I've had some good conversations early this morning. It is between Mitch and Harry. And I think people want to see that come to fruition," said Corker, a member of the Senate Banking Committee.