Dempsey scored 17 Premier League goals for Fulham last season but wants to play Champions League football.
“Clint Dempsey wants to move. He doesn’t want to commit to this club and, while I would like to keep him, it’s impossible because he wants to move,” Jol told a news conference ahead of his side’s Premier League opener at home to Norwich City on Saturday.
“He told me that he wants to go to a Champions League club – he said it last year, he said it in the summer, and he said it again.
“We’ll have to wait and see what happens but it’s a sad situation for us and it’s almost embarrassing,” Jol added.
“We’ve got a chairman who is strong and if we get the right price for Clint then we will sell him. If we don’t, then he will stay here. We won’t let Clint Dempsey go on the cheap, that’s for sure.”
United States head coach Juergen Klinsmann said in May he hoped Dempsey would move to a Champions League club after his fine season.