Speculation has been rife this summer that the 29-year-old is set to link up with the Reds, which was fuelled on Wednesday after a report on the club owner's official website suggested a deal was complete.
An article linked to the Fenway Sports Group (FSG) homepage, www.fenwaysportsgroup.com, said that Liverpool had "added Clint Dempsey to a team that came within a game of winning the FA Cup".
Any mention of Dempsey, who has a year left on his contract, was later removed from the article hosted on FSG-owned website www.NESN.com.
Fulham said the report was unfounded and issued a warning to any interested clubs.
"We have received no offers from any club for Clint Dempsey," a club spokesman said. "We would discourage any club from making a bid for him."
It is understood the two clubs had a conversation about a possible move for Dempsey earlier in the summer but that has not been followed up by any official approach, contrary to reports.
Dempsey has been with west London side since 2007 after joining from Major League Soccer's New England Revolution.
The Texan has established himself as one of Fulham's key players and last term won player of the season, as well as finishing fourth on the Football Writers' Association's Footballer of the Year list.