The Nigeria international enjoyed an impressive debut season in the Premier League last term and finished as the Baggies' top scorer.
His exploits have seen the striker linked with several clubs during the summer and Wigan Athletic had a ?1.5million bid rejected before the weekend.
Baggies boss Roy Hodgson laughed off the size of the Latics' offer and confirmed he is hoping to secure Odemwingie on a new deal at The Hawthorns, where he is still under contract for the next two years.
However, it is understood those negotiations have reached an impasse, with Newcastle and Spurs also showing an interest in the 30-year-old.
Odemwingie missed West Brom's opening game of the season against Manchester United on Sunday through injury and Hodgson insisted after the 2-1 defeat that the former Lokomotiv Moscow forward is not for sale.
But Monday's papers have suggested Tottenham chief Redknapp may put a bid on the table if Peter Crouch leaves White Hart Lane in this window.
Source: Team Talk
Source: Team Talk