Feghouli only moved to the London Stadium in the summer last year, signing a three-year contract after his deal at Valencia expired, but his stay could already be coming to an end.
The Algeria international has made nine Premier League appearances this season, mostly from the bench, and was given a harsh red card on his first league start against Manchester United on January 2.
He has struggled to impress Hammers' manager Slaven Bilic and there are now reports claiming a move away before the end of the January window is on the cards.
Roma are believed to be the front-runners for the 27-year-old's signature with the Italian club preferring a loan deal until the end of the season, with an option to buy in the summer.
West Ham are said to want around the £7-8million mark to sell Feghouli and this would represent a good deal for the Hammers, who snapped him up on a free transfer.