The 25-year-old has made 80 appearances in total for the Rams and he earned himself a call-up to Fabio Capello's England squad in 2010.
Team-mate and fellow keeper, Adam Legzdins, has also been made available for transfer following the signing of Lee Grant from Burnley.
Derby have made seven first-team players available for transfer this summer and Clough insists he will not stand in the way of either goalkeeper heading for the exit.
"If offers come in, Adam and Frank will both be allowed to leave," he told the Derby Telegraph.
"We would love to keep one of them as the number two but they don't want to do that.
"Both have had a taste of first-team football. Once you have had that taste, you don't want to sit on the bench.
"I think they are two very good keepers with huge potential."