Fulham fined Clint Dempsey on Friday after the United States international refused to play for Fulham, manager Martin Jol said Friday.
Jol confirmed that Dempsey will not start Saturday in Fulham's Premier League season opener against Norwich City.
Dempsey, who had 23 goals in 46 games to become Fulham's top scorer last season, is seeking a move to a Champions League club.
"Clint Dempsey wants to move," Jol said. "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. 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.
"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."
In an apparent response to Jol's comments, Dempsey later made two short comments on his Twitter account.
"There are two sides to the story," he tweeted, before adding: "The truth will come out soon."
Dempsey has been at Craven Cottage since 2007 and his contract expires next year.
The American was left out of the club's preseason training camp in Switzerland amid speculation about his future.
"Clint was not involved over the last four weeks, so he is not going to be in the squad," Jol said.
Liverpool has been the club most strongly linked with Dempsey, with manager Brendan Rodgers having confirmed an inquiry was made.
At one stage, the website for Massachusetts-based TV station NESN, owned by Fenway Sports Group, published a story suggesting the deal was done, but the posting was removed soon afterwards.
"That was very disappointing," Jol said. "There was never an offer. Clint himself told everyone he was going to Liverpool before he came back, so we really thought there was quite a firm interest in him.
"Even (Rodgers) told everyone he was interested in Clint Dempsey, but our people never had an offer on the table, so it's almost embarrassing. If you have shown interest in a player, especially in England, you have to follow it up with an offer. They didn't."
Jol also expressed his disappointment at the recent conduct of Moussa Dembele's agent, denying that there had ever been interest from Real Madrid. Jan de Visser, Dembele's representative, had made comments to Dutch newspaper De Telegraaf indicating that a bid had been made by the Spanish side.
"I spoke to his agent and I said to him it's not the cleverest thing to do, to speak about players. There was no offer on the table (from Madrid) and hopefully the situation will stay as it is. Hopefully Dembele will stay here," said Jol.
"There was one low bid from one Premier League club, very low. Moussa is quite happy here. He wants to play here and if something happens, we will have to wait.''
Information from The Associated Press and Press Association was used in this report.