Hodgson wants Odemwingie to stay
Odemwingie was Albion's top scorer last season, his 15 goals helping to preserve the club's Premier League status.
The Nigeria international has struggled to recapture the same form during the current campaign but remains pivotal to Hodgson's plans.
Hodgson said: "I'm not aware of any interest in Peter. We don't need to sell him, we don't want to sell him.
"We can't stop clubs making offers. One club rather cheekily early on (in the transfer window) said they'd like to loan him for a few months but I think that was a semi-jocular approach."
Hodgson, who saw an initial bid for Birmingham defender Liam Ridgewell rejected on Tuesday, will not make any panic signings this month.
He said: "I've said all along that if the player isn't there, then there is no desperation or panic on my side.
"You just don't want to bring in extra bodies for the sake of it. I believe in my team and we have players who can get us home this season."
Midfielder Paul Scharner (Achilles) and defender Billy Jones (hamstring) are doubtful for Saturday's match at Stoke.