The Nigeria striker has scored 30 goals in 67 starts for the Baggies since signing from Lokomotiv Moscow in 2010 but dramatically fell out of favour in January when he tried to engineer a move to QPR without permission.
That move never materialised and although Odemwingie made up with boss Steve Clarke and returned to the first-team, he appears certain to leave the club this summer.
Palace made a move to sign the 31-year-old during the January window but he was unwilling to drop down to the Championship.
However, following the Eagles' play-off win over Watford on Monday, the London club can now offer top-flight football.
It is believed Palace boss Ian Holloway is ready to offer West Brom in the region of £4million to lure the striker to Selhurst Park.