The American striker's contract expires at the end of next season and Martin Jol is keen to keep his key players at Craven Cottage as they bid for European football
The USA international is top scorer for Martin Jol’s side this season with 18 goals, and bagged a brace in their 5-0 demolition of Wolves last Sunday.
Jol is confident Dempsey will pen a new deal, with his contract expiring at the end of next season, despite the 29-year-old admitting he wants to play in the Champions League before he retires.
The Fulham boss told reporters: “We are talking to him. At any club, you want to keep your best players so that is what we try hard to do.
"He is here for at least another year, so that is not a big problem. The problem is that we want to keep him here for longer. But the difference is not very big.
“He has 17 months left and we want to keep him here for the next three years.”
Former Tottenham manager Jol has guided Fulham into the top half of the Premier League table, where they currently sit eighth, and he admits Dempsey has been a key element in their success.
He said: "If Clint Dempsey wasn't here, we wouldn't be in this position because we have had to rely on him a lot of times to score goals.
"I hope the four or five players we are talking to will stay. I am confident they will. They realise it is a very good club."