Jol hoping Dempsey will stay
Dempsey, 29, has scored 22 goals this season and is one of the main reasons Fulham are sitting in tenth place in the Premier League table without any relegation worries.
Dempsey, however, has one year left on his contract and Jol, who lost Dimitar Berbatov to Manchester United for £30 million when he managed Tottenham, fears that a big club could come in with an offer for the United States international that Fulham could not turn down.
Jol said: "If you have a year to go it is hard to keep someone. If you want to keep him on a contract until it will finish that will be a difficult situation for him and for us.
"That is the main priority I want to focus on. Can we keep him? We have made him a good offer and we have to wait and see until the summer, but I told him yesterday that I would love him to stay here at least as long as I am here.
"He's had some season. He can score from all angles in the box and he can even score when he is not playing up front. I am very happy he is there. We are talking to him and hopefully we will get it right."
Jol, recognising that interest in Dempsey is likely to peak in the summer transfer window, added: "It depends on the club that is coming in. At Spurs I had the same situation with Berbatov, if it is a big club then maybe you have a little problem."
Jol also faces losing the possibility of losing 35-year-old captain and playmaker Danny Murphy, whose contract is up this summer. He has been linked with a coaching role at QPR.
Jol said: "He is a free agent and he can do what he wants to do, but we talk to him as well. He could do a similar (coaching) thing here."
Fulham resume their Premier League season against resurgent Wigan on Saturday after an impromptu break last weekend caused by rearranged fixtures.
Strikers Pavel Pogrebnyak and Andrew Johnson return to the squad after recovering from ankle and thigh injuries respectively but Jol is under no illusions that his team will face a battle against a Wigan side who have put breathing space between themselves and the relegation zone after beating Manchester United and Arsenal in the past ten days.
Jol believes Wigan's Spanish boss Roberto Martinez, a huge admirer of Barcelona's passing style, has had to curb his attacking tendencies to put some steel into the Latics.
Jol said: "They still need three or four points so they will fight for their lives. Bolton were in the same situation and we did well so hopefully we can keep the initiative. We have to be patient.
"Wigan did well at the right time of the season. They could get out of trouble now. They like to play but when they did that they didn't have the points. They have changed their style. They defend in numbers and they have got three players up front who do all the damage.
"They play compact now, like they did against Arsenal. There was no space on the flanks, there was no space in the middle. I went to the Emirates and saw that game. They are a hard team to beat these days."