Jol blasted fans' chants about the American midfielder and hopes that he can persuade last season's top scorer to remain at Craven Cottage, despite Dempsey's desire to leave.
Dempsey, 29, scored 17 league goals in the previous campaign and has been linked with a move, with Liverpool thought to be the main contender. However, Jol recently claimed that the Reds had made no bid, and that the situation was 'embarrassing'.
"There is one season to go on his contract and no-one has come in for him," the Fulham boss told reporters. "To say he refused to play is probably a bit harsh, but he wanted to move. If you want to move, you don't want to take risks so you don't want to play in case you get an injury.
"For me that was a very awkward situation and it was for him as well. There is nothing on the table from Liverpool. Maybe Clint knows more than us but we feel he should stay if there is no other bid."
Dempsey was absent from the Cottagers' matchday squad for the 5-0 win over Norwich. Cottagers fans sang "Are you watching Clint Dempsey?" towards the end of the game, but Jol feels the chants were unfair.
"I don't want to hear the fans chanting against him because he was a terrific player for us," the Dutchman said. "He was the most productive midfield player in the whole league last season and hopefully he will play for us again."
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