The Hoops manager Harry Redknapp has made no secret of his desire to sign the Nigeria international as he bids to add much-needed fire power to his squad.
However, the Baggies have already rejected a reported £2m offer from the west London outfit for the striker, and West Brom sporting director Richard Garlick insisted Odemwingie won’t be leaving this month.
“Last summer there were supposedly players leaving but we kept hold of most of them,” Garlick said.
“We don’t have to sell any of our players. It’s only on our terms.
“It’s well documented about Peter. We had an offer and we don’t intend to sell any of our players.
“When an offer comes in, we speak to the player out of courtesy. We’ve had that chat with Peter and he knows the situation.”
Garlick also revealed West Brom manager Steve Clarke is unlikely to strengthen his squad in January, with the Baggies currently in eighth position.
“We’re happy with the squad we’ve got and there are no immediate plans to bring anyone in,” he added.
“If an opportunity presents itself, then we will look at that, but we’re looking more towards the summer.”