The Reds went after the USA international - now with Tottenham - in the offseason and prematurely reported that he had signed at Anfield when an article on the Fenway Sports Group website claimed he had joined.
Fulham manager Martin Jol suggested that Liverpool had gone about their business poorly, prompting the Southwest London club to lodge an official complaint but that has now been withdrawn following the Anfield explanation.
"Fulham can confirm that it has today withdrawn the complaint made against Liverpool FC in regard to the Merseyside club's inappropriate actions surrounding interest in Clint Dempsey over the summer," read a statement on Fulham's official website.
"Liverpool's chairman Tom Werner apologised personally to Mohamed Al Fayed, stating that his club were wholly responsible for unprofessional behaviour toward Fulham and emphasised his regret for the entire episode.
"In a letter from Liverpool to Fulham's CEO Alistair Mackintosh, Tom Werner's praise of the magnanimous gesture from the chairman was reiterated, as was the club's assurance that the conduct of Liverpool was simply not acceptable.
"The chairman decided that this sincere action was enough, and as a gesture of goodwill, instructed that all complaints against them be dropped."