QPR had a bid for the striker turned down earlier this month, though it was understood Odemwingie wanted the opportunity to discuss a move.
The 31-year-old has now put in writing his wish to leave the Hawthorns two-and-a-half years after his arrival from Lokomotiv Moscow, but his request has been turned down by the Premier League club.
Albion's sporting and technical director Richard Garlick said: "Peter is hugely popular with our supporters and it is disappointing that he has decided to hand in a transfer request.
"It was immediately turned down and has done nothing to change our stance during January. Peter is under contract until the summer of 2014 and we have no need or desire to sell our core players.
"We want to keep the squad intact to enable us to build on an encouraging first six months of the season."
Odemwingie top-scored for Albion last season, but his equaliser against Aston Villa last weekend was his first goal in 10 games.