Albion had been optimistic of bringing midfielder Gera, who is out of contract, back to the Hawthorns and had held initial talks with the player. But Jol is also an admirer of the Hungarian international and tried to sign the 32-year-old from Ferencvaros when manager of Tottenham.
Gera's agent, Vladan Filipovioc, told Hungarian newspaper Nemzeti Sport: "Martin Jol knows and likes Gera's style."
He added: "When he was manager of Tottenham, he wanted to sign Gera. He would probably like to work with him now.
"Until Gera signs his new contract, anything can happen. It could be that he even stays at Fulham."
Gera made 155 appearances for the Baggies before moving to Fulham during the summer of 2008 when Roy Hodgson - now Albion's head coach - was manager.
West Brom are stepping up their search to sign a new striker after losing out to Swansea in the race for Watford's Danny Graham who completed a ?£3.5 million move to Wales to yesterday.
Albion had previously had a £2.5m bid rejected for the former Middlesbrough man.
Source: PA