Manager Martin Jol told the media that last season’s top goalscorer is keen to switch to a Champions League-chasing club and has subsequently withdrawn from Saturday's matchday squad to face Norwich City.
However, Dempsey has seemingly rejected these assertions via Twitter.
"There are two sides to the story," Dempsey wrote. "The truth will come out soon."
The 29-year-old's future has been up in the air ever since he pulled out of the club's pre-season tour of Switzerland last month, as exclusively revealed by Goal.com, in an attempt to force through his exit, with Liverpool long-term admirers of the player.
|HOT SHOT CLINT
|50/1||Clint Dempsey is 50/1 to be the Premier League's top scorer with Bet365|
However, Jol confirmed at the same press conference that Brendan Rodgers' side never cemented their interest with a concrete offer - to the disappointment of Dempsey.
"There was never an offer," Jol told reporters. "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."
"Maybe Liverpool will come back. I can assure you that our chairman is strong enough. At first we didn't want to get rid of him, later on we had to change our position - but our view is that we won't let Clint Dempsey go on the cheap, that's for sure.
"If we get the right price for Clint we will sell him. If not, he will stay. We want to keep him but it's impossible because he wants to go. Clint wants to go to a Champions League club."