Current Baggies boss Roy Hodgson signed the Hungary international when in charge of Fulham in the summer of 2008.
He wants to be reunited with the 32-year-old and it is understood that initial talks have taken place.
Sown the red card? Gera may have played his last game for the Cottagers
Gera is believed to be willing to return to West Brom where he was a fans' favourite. He made 155 appearances in his four-year spell at the Hawthorns after a ?1.5million move from Ferencvaros in 2004.
Hodgson has already signed Ipswich centre-back Gareth McAuley and Preston full-back Billy Jones since the end of the season.
He is also still interested in Blackpool midfielder David Vaughan but may lose out in the race to sign Watford striker Danny Graham, who has also been targeted by Swansea and Cardiff.
Fans' favourite: Gera has made as many friends at Craven Cottage as he did at the Hawthorns
Meanwhile, skipper Chris Brunt appears content to commit his future to the Baggies.
He said: 'I've got a contract at Albion and until someone tells me otherwise, I'll be be playing here.
'I enjoy playing for West Brom, have got a decent relationship with the fans, and know the ins and outs of the club.' Make me the new manager, skipper Murphy urges Fulham hierarchyHands off! Hodgson offers Odemwingie new deal to ward off WengerAll the latest Fulham news, features and opinionAll the latest West Bromwich Albion news, features and opinion
Explore more:People: David Vaughan, Roy Hodgson, Danny Graham, Gareth McAuley Places: Cardiff, Hungary