The 32-year-old Croatia international has made just eight Premier League starts for the Cottagers since joining them on a free transfer from Hamburg on a one-year deal last July.
He has made a further 10 appearances from the bench but has been kept out of the side by Dimitar Berbatov, who followed him into Craven Cottage in August.
However Jol remains keen to retain Petric, who has scored five goals this season, after also working with him at Hamburg.
"Petric is one we would like to keep," the Dutchman told the Fulham Chronicle.
"He wants to play and because of Berbatov he couldn't. He was probably the most effective player in England - he scored goals and didn't play a lot."