The American attacking midfielder is understood to be ready to leave Fulham for a Champions League-standard club and the Reds manager has confirmed his interest
Liverpool manager Brendan Rodgers has confirmed that the club have made an enquiry for Fulham forward Clint Dempsey.
The former Swansea City boss was already known to be trailing the USA international, who notched an impressive 23 goals for the Cottagers last term, as Goal.com revealed on Monday that the Reds are preparing a £5 million bid but waiting until Andy Carroll's future is resolved to make a move.
Rumours circulated on Wednesday that a move was close to completion and, speaking on the club's pre-season tour of Boston, Rodgers admitted to his interest in Dempsey but was sure to clarify their current stance.
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"Clint is a player we've enquired about, it is as simple as that," the Reds coach told the club's official website.
"Ian Ayre, our managing director, has spoken with the club [Fulham] to see what the position is. That is where we're at.
"He's a very talented player but we don't like to talk about other clubs' players."
Rodgers completed his first business as Liverpool boss on Friday with the signing of Roma forward Fabio Borini for a reported £11m, with Arsenal wideman Theo Walcott also heavily linked with a move to Anfield.
But, whilst speculation mounts over the future of £35m striker Andy Carroll, the Ulsterman moved to quash rumours of a possible loan move to former club Newcastle.
"There has been a lot written and spoken about him but first and foremost Andy is a Liverpool player," Rodgers added.
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"To consider a loan period for someone the club spent £35 million on isn't something we're looking to do at this moment in time.
"Andy will be the same as every other player - if there's ever an offer that comes in we'd look at it as a club and see if it's going to be worthwhile for the club and the team as a whole.
"The club invested £35 million in him. People talk about whether he can fit into my style or not, but if you're a club and you spend £35 million on a player you'd like to think he can fit into whatever style the team plays.
"He's a good player. He'll join the rest of the group next week and we'll take it from there."