The 31-year-old forward, who has scored five goals in 18 Premier League appearances this term, has been the subject of strong interest from QPR.
Goal.com exclusively revealed last week that Odemwingie was on the verge of handing in a transfer request and the forward has now made his stance clear to the club.
However, the Baggies' sporting and technical director Richard Garlick has insisted the Hawthorns outfit will not consider losing their "core" players.
“Peter is hugely popular with our supporters and it is disappointing that he has decided to hand in a transfer request," he told the club's official website.
“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."