The 31-year-old made his desire to leave known earlier today, but the Baggies have reiterated that they will not sell any players this month.
Sporting and technical director Richard Garlick told the club's official website: "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 has been heavily linked with a switch to Queens Park Rangers.