The 26-year-old only moved to the Baggies last summer for a then club-record fee of almost £10m, signing from Dynamo Kiev on a three-year-deal.
But he made just 13 starts in the Premier League last season, struggling to make an impact under Alan Irvine and his successor Tony Pulis.
Ideye was also the subject of transfer interest during the January window, but a move did not materialise.
He has featured just once this season, playing 90 minutes in the Capital One Cup win on penalties over Port Vale.
Ideye is a Nigeria international with 20 caps and five goals for his country, and began his career with Nigerian Premier League team Bayelsa United.
He first moved to Europe in 2008 with Swiss side Neuchatel Xamax before moving to French Ligue 2 club FC Sochaux-Montbeliard in 2010.