The American forward has 16 months remaining on his current deal and could be reluctant to sign an extension which would rule out a move to a bigger club
The United States international, who increased his goal tally for the season to 13 against Norwich at the weekend, has 16 months left on his current contract with the Cottagers.
However, he is reportedly reluctant to commit to a deal which, at the age of 29, would scupper his chances of playing for a Champions League side.
Jol was unconcerned by the prospect of delayed contract talks though, warning Dempsey that players who leave the club rarely go on to do better.
The Dutchman said: “It’s the sort of principle of this club and I think it pays off. How many players will go on a free? I can’t predict the future but I hope he will stay.
"I think if you come to our lodge, the grass is very green and there are not a lot of players over the past five or six years to have left Fulham and done well.”
The American scored one and set up another at the weekend and praised the character his team-mates showed during the 2-1 win at Craven Cottage.
Dempsey said of the win: “We had our backs against the wall but we showed character".
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