West Bromwich Albion are keen to offload the Nigeria forward, who fell out of favour after a proposed move to Queens Park Rangers collapsed in January, although the Midlands club are hoping for a fee closer to £2.5m and would prefer to sell him overseas.
It is understood that Odemwingie's preference would be to remain in the Premier League, with Palace representing the best chance of that happening. The Fulham manager, Martin Jol, had considered trying to bring Odemwingie to Craven Cottage but it seems unlikely that his interest will translate into a formal offer.
Palace will almost certainly have to raise their bid for Odemwingie for Albion to do business, although with the transfer in everyone's best interests, it is likely a compromise will be reached.
The 31-year-old, who has 12 months remaining on his contract at The Hawthorns, has no future with Albion. He has been made to change in a separate dressing room to the rest of Albion's first-team squad while his training is restricted to individual work, away from the rest of the players.
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