The Nigerian irked the Baggies during the January transfer window by driving to Loftus Road in an attempt to force through a deadline day move to QPR.
These actions saw his status as a key first-team player evaporate during the latter half of the campaign, putting his Premier League future into doubt.
But, Swansea are willing to offer the 31-year-old an escape route from The Hawthorns, with manager Michael Laudrup ready to take a risk on the fiery attacker.
The Swans are set to embark on a huge summer as they go about building a squad capable of competing in the Europa League, while maintaining Premier League safety.
With just 12 months remaining on his contract, Odemwingie is expected to be moving on in the coming months, and the Baggies are unlikely to put up much of a fight.
Laudrup sees his experience and versatility as two characteristics that outweigh his questionable attitude, and believes that he can slot into the first-team at the Liberty Stadium easily.
Odemwingie made 25 Premier League appearances last season, notching five goals in the process.
Does Peter Odemwingie deserve a second chance? And could he be a good fit at Swansea?
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