The Cottagers are dealing with the repercussions of the decision by Reds manager Brendan Rodgers to publicly voice his interest in Dempsey last month.
Dempsey has been agitating for a transfer to Anfield since, but an official offer for the ?7.5million-valued American forward has yet to be received, leaving player and coach in limbo.
Fearing that the club's prized asset has been distracted and is unfit to play, manager Martin Jol dropped him for last weekend's 5-0 drubbing of Norwich and will omit him from Saturday's squad to face Manchester United.
Jol is frustrated that he has been left with an unsettled player, but has offered an olive branch to Fulham's top scorer of last season.
"Mentally Clint wants to move, he doesn't want to stay here. His head was turned and that was the problem," Jol said today.
"It's a problem and a situation you don't want. It's not something you can talk to a player about every day because he doesn't want to.
"I don't know if he'll remain a Fulham player. I'd love to keep him, but I'm not sure.
"Hopefully if he stays, then in the next couple of weeks he will change his thoughts about us.
"With me there's no problem and I don't think there's a problem within the team over him."
Jol denied Dempsey had refused to play for Fulham again, instead declaring it was his decision to drop the 29-year-old, who has entered the final year of his contract.
"I never said he's gone on strike," he said.
"It started during our pre-season tour to Germany. I was probably a bit naive, asking 'Clint, do you want to start?'. All he said was 'you know what I want'.
"This hasn't caused any disruption to the squad because of the decision I made in Germany not to play him.
"After that it was very difficult to communicate. He was not committed to the team.
"For us it would have been better had Liverpool followed it up with a formal bid, but they haven't."
Fulham have expressed their concern over Rodgers' conduct to the Premier League, who are to investigate the issue.
"The Premier League has received a complaint from Fulham regarding certain comments made by Liverpool officials and is currently looking into the matter," read a statement issued by the Premier League.
Jol advised Dempsey to look to Robin van Persie's ?24million move from Arsenal to Manchester United for instruction on how a transfer should be completed.
"There are always players in football like Van Persie who want to move, but they keep quiet," he said.
"This was different. Although we like to keep everything under the surface, it was impossible. Van Persie did the right thing.
"I always hope for players to keep a low profile and wait for what will happen. It's better for the manager and club."
