The Scotland international was left out of West Brom's 18-man squad for their New Year's Day defeat by Fulham despite being fit.
It is understood he and the club have come to a mutual agreement that he can leave if a suitable deal is agreed during the transfer window.
Dorrans signed a long-term contract in July 2010 which tied him to the club until the summer of 2015, shortly after West Ham had several bids for the player rejected.
Dorrans has 18 months left on his contract but West Brom retain the option of another year so are likely to seek a sizeable fee for the 25-year-old, having rejected a £5million offer from the Hammers.
Dorrans joined the Baggies from Livingston in 2008 and has made more than 130 appearances for the club, 12 of them since Steve Clarke took over as manager in the summer.
West Brom were unavailable for comment.