The American is the club's top goalscorer this season and Jol admits that he is desperate for him to sign a new deal.
Jol said: "We offered him an improved deal last week. He's our top goalscorer and that tells you everything.
"I can't look to the future but I hope he will [stay]. If you come to our lodge the grass is very green and there are not many players who have left Fulham over the last few years who did well.
"Hopefully I can convince Clint that he should stay with us for another couple of years."