The controversial Nigerian is believed to have little future at the Hawthorns, with the Baggies having not fully forgiven him for his January antics.
The 32-year-old openly chased a move to now relegated QPR, and even drove to Loftus Road in a bid to push through the deal.
He was eventually forced to stay in the Midlands, but manager Steve Clarke has now strengthened his squad which has left Odemwingie some way from the starting XI.
Stoke, Cardiff and Swansea are all keen to take advantage of the situation, and are willing to pay in the region of £2m to secure a deal in the coming days.
Swansea could be the most appealing destination, with Michael Laudrup’s men set for a Europa League campaign.
But, their South Wales rivals are hopeful that an increased chance of regular first-team action could swing the odds in their favour.
Meanwhile Stoke boss Mark Hughes wants to make Odemwingie a part of his revolution at the Britannia Stadium.
The versatile attacker himself is believed to be happy to move on, and is keen to stay in England.
Does Peter Odemwingie deserve a Premier League lifeline?
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