There has been speculation that Odemwingie could be heading to Craven Cottage with winger Damien Duff and defender Chris Baird moving in the opposite direction. However, Hodgson still regards Odemwingie as a key figure even though he has struggled to reproduce the form which brought him 15 goals last season.
"There is no truth in it. We've had no contact with Fulham - or any other club - regarding Peter," said Hodgson.
"He is not a player we want to sell and the story is a bit of a waste of breath to be honest.
"I've said many times that we don't want to sell Peter."
Hodgson is also close to abandoning his attempt to sign Birmingham defender Liam Ridgewell after confirming an initial bid had been rejected.
He said: "We made our bid and we perhaps have to start looking elsewhere.
"I don't think the club is anxious to improve the bid. As far as I was concerned, it was an idea that came up.
"I thought it was a good idea at the price. We thought it would be a possibility. But if it is not a possibility, we will have to move away."