Jol admits Fulham will struggle to keep Dempsey
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.
"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."