"These stories are complete fabrication," Sheehan told skysports.com.
"Leicester assure me no bid has been received and no one at Villa has contacted me to see if Andy would even be interested in a move.
"I think someone has used Andy's name to maybe try to force another deal through, so it's a well deserved compliment that they felt Andy's was the most appropriate name to use.
"I would like to assure all the Leicester fans that Andy's immediate response without any hesitation was that he wanted to stay at Leicester, no matter who came in for him. It's never about money and it's not about Villa.
"Andy is extremely settled and is in a good place mentally and physically. He loves the club and the fans and is looking forward to carrying on where he left off last season.
"There is now increased competition in the middle of the park and that is what Andy needs to concentrate on so this all needs to be nipped in the bud."