The Welsh side are understood to be competing with Swansea and Stoke to land the forward, who is firmly out of favour at The Hawthorns.
West Brom are believed to be holding out for a fee of over £2million for the Nigerian international.
Odemwingie has been frozen out by Steve Clarke since he tried to force a move to Queens Park Rangers in January and was subsequently punished for his indiscipline.
The Baggies bolstered their attacking options with the capture of former Real Madrid striker Nicolas Anelka earlier this month
And they look set for a busy transfer deadline day, having also been linked with moves for Everton's Victor Anichebe and Sunderland's Stephane Sessegnon.