"I was shocked when I was told of what was reported in a Sunday newspaper," Hodgson told the club's official website.
"Jimmy's importance to us after his return to fitness can not be underestimated.
"He was integral to our survival and is a very important player for this football club.
"I can understand that the Fulham fans would be understandably perturbed to read such nonsense, but I can assure them that it is nonsense of the highest order, with no substance whatsoever.
"Jimmy Bullard is a key player for Fulham and I hope that he will remain so for many seasons to come.
"We are looking forward to making some additions to the squad over the coming weeks which is an exciting time for the club and Jimmy Bullard will be playing alongside whoever they may be."