Dempsey turned in another outstanding performance with two goals in a comfortable 3-0 win at Bolton in the Premier League on Saturday. The versatile American, who struck with a superb long-range free-kick and a firm header, has now scored 21 times in all competitions this term.
With just one more season remaining on the 29-year-old's contract, Fulham accept he could become an attractive target for other clubs and are keen to tie him to a new deal.
Jol said: "I can't foresee the future. We want to keep him and hopefully he wants to stay. We have offered him a very good contract. He knows he is very appreciated at our club, so hopefully he will stay.
"If we want to be a top side we need players who can score more than 20 goals in all competitions. I have always had that - I can remember Luis Suarez scoring 53 goals for me at Ajax.
"He's not at that level yet but of course it is a different league and, for a wide midfield player who can play up front and score that many goals, it is unbelievable."
Dempsey said after Saturday's victory that he was pleased with his goal return this season.
Dempsey said: "I hadn't got too many goals away from home this season. It is good to add to that and good for us to get three points away from home. We are excited about that, we can add to that.
"I have never got these type of numbers before - 21 for the season, 15 for the league. I am happy with that return and we have still got some games left, so hopefully I can chip in with a few more."