Former Fulham boss Hodgson has played down speculation Odemwingie could be heading to Craven Cottage with winger Damien Duff and defender Chris Baird moving in the opposite direction.
Hodgson still regards Odemwingie as a key figure even though he has struggled to reproduce the form which brought him 15 goals last season.
He said: "There is no truth in it. We've had no contact with Fulham - or any other club - regarding Peter.
"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."
Ridgewell was the subject of an enquiry from Albion during the last transfer window and submitted a transfer request but he remains a Blues player at present.
Hodgson is looking for Albion to repeat the defensive solidarity that earned them a 1-1 draw at Stoke last season.
He said: "The Stoke challenge is no longer unique because we have come to terms with it after four years so everyone knows what they are good at and what problems they cause.
"You hope you have got the players who can deal with the challenge because you can't stop the ball being whizzed into your box and you can't stop them sending forward six footers.
"You have to have the players who can deal with that and not surrender to the pressure. We have sufficient ability to deal with it and we dealt with it pretty well last season."
Hodgson confirmed defender Gonzalo Jara-Reyes will remain part of his plans after he pleaded guilty on Friday at Brighton Magistrates court to driving while disqualified and driving without insurance.
But the club will stage an internal inquiry into Reyes' actions which occurred while he was on loan to Brighton earlier this season.