Nigerian Odemwingie was recently the subject of a bid from bottom side Queens Park Rangers which was turned down but he has since told the club he wants to leave.
"Peter is hugely popular with our supporters and it is disappointing that he has decided to hand in a transfer request," West Brom's Sporting and Technical Director Richard Garlick told the club's website on Friday.
"It was immediately turned down and has done nothing to change our stance during January.
"Peter is under contract until 2014 and we have no need or desire to sell our core players."
Tashkent-born Odemwingie was signed from Lokomotiv Moscow in 2010 and scored 15 league goals in his first season.
- Sports & Recreation
- Queens Park Rangers