Queens Park Rangers are known to be interested in the Nigerian striker, with some reports claiming that he is keen on a move to the capital.
However, because of injuries, Foster has admitted that the Baggies cannot afford to let any players leave.
"We can't afford to let anybody go. We have been struggling [with injuries]. We have had 13 or 14 players in training at times. Hopefully [Odemwingie] won't be going anywhere," said Foster. "He has always got that ability to score goals for us when it matters. He can be frustrating at times, but other times he can be magical.
"Sometimes everyone says 'just try to shoot'. I know sometimes it will go wide or over the bar, but he can unleash and when he does, they can be unstoppable.
"That's the beauty of him, he can frustrate you, but has so much skill and ability."
Odemwingie has scored 31 goals in 83 appearances for West Brom.