The American midfielder had a superb season at the Cottagers last term, scoring 17 league goals in 37 appearances, and he has been linked with a move to Anfield in recent weeks.
Liverpool manager Brendan Rodgers confirmed the Reds’ interest in the 29-year-old earlier in July, but Jol is desperate to see Dempsey remain at Craven Cottage.
“I don’t want to talk about that. I love Clint, he scored a lot of goals and I want to keep him,” Jol told the Fulham and Hammersmith Chronicle.
Jol has seen Bobby Zamora and Andy Johnson both join Queens Park Rangers over the past six months, while Pavel Pogrebnyak moved to Reading this summer.
The Fulham boss says he is looking to strengthen his attacking options, with Hugo Rodallega arriving from Wigan Athletic and Mladen Petric swapping the Bundesliga for the Premier League.
“We’re still looking to strengthen because we lost three strikers,” Jol said. “Bobby in January and Andy and Pogrebnyak. We’ve got Rodallega and Petric and maybe we’re still on the lookout for another one.
“Rodallega is fit now. He had an ankle injury but trained for the first time on Friday. Petric is looking pretty good as well.
“Rodallega is similar to Andy Johnson. He’s got a lot of pace to stretch defences and can also play on the left. Petric is a number nine but can play off a big man as well. He’s really versatile. I know him from Hamburg and he was a very talented boy.”
Former Liverpool midfielder Danny Murphy also left Fulham after five seasons at Craven Cottage, and Jol hailed his former captain’s contribution to the club.
“I was sad that Danny went,” Jol said. “We agreed terms then Blackburn offered him two years. That happened within one or two hours so I was not happy with that. I wish him all the best because he was a great servant for this club and I wanted to keep him.
“[Mahamadou] Diarra can play that role and Dickson [Etuhu] is still here, but we’re certainly looking for one midfield player.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news