Odemwingie is out of favour at the Hawthorns and West Brom are willing to offload the Nigerian.
The 31-year-old has found himself down the pecking order after failing to force through a move to Queens Park Rangers on transfer deadline day in January.
Palace boss Ian Holloway is now ready to offer Odwemwingie an escape route out of West Brom as he looks to bolster his attacking options.
Holloway has already brought in Dwight Gayle from Peterborough this summer and he sees Odemwingie as an ideal foil for the young forward in a new strike partnership.
Talks are thought to be at an advanced stage between both clubs as Palace look to add to their ranks as they prepare for life back in the Premier League.