Hodgson has revealed he has turned down a loan bid for the Nigeria international striker.
The 30-year-old has long been linked with a move to Fulham.
“I’m not aware of any interest in him,” said Hodgson. “One club rather cheekily said they’d like to loan him for a few months quite early on but I think that was a semi-jocular approach. We don’t need to sell.
“We can’t stop speculation. We can’t even stop other clubs making offers, which they haven’t done yet. That doesn’t mean to say that one day we won’t receive an offer for one of our players, Odemwingie or anyone else. When that day comes you deal with it.”