The 30-year-old was subject to a recent bid by Wigan Atheltic, but Hodgson dismissed the offer as laughable.
"Peter is not for sale," he said. "If you had seen the size of the bid, you would probably have been laughing all the way out of here.
"I don't understand teams to put in bids which are so obviously ludicrously far away from what the player's value is."
Hodgson was speaking after his side lost 2-1 to Manchester United at the Hawthorns.
Odemwingie was the Baggies' top league scorer last season with 15 goals after a move from Lokomotiv Moscow.