The American has since been training alone ahead of the new Premier League campaign.
A club statement read: "Martin Jol confirms Clint Dempsey wishes to leave the club."
However, Jol has told Liverpool that Fulham will only do business at the right price.
"If we get the right price for Clint we will sell him," said the Dutchman. "If not, he will stay. We have money to invest, but only in the right players."
Dempsey scored 17 Premier League goals last season.