The Division Two club's assistant manager Kenny Jackett told skysports.com Carlisle would do a great job if he were to move to Leeds, but he did not know about any bid.
"Nothing surprises me in football," he said.
"If Clarke did go he would do a great job. But obviously, I haven't heard of Leeds' interest and I hope he stays."
The defender is out of contract in the summer and returned to training late last year after undergoing treatment for alcohol problems. A fee in the region of £200k is being reported.