Odemwingie is on the fringes at West Brom after trying to force a move away from the club last month.
It would remain to be seen if he wants to return to Russia however, as he was the victim of racial abuse during his last spell there.
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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?