It has also been reported that the Reds' managing director Ian Ayre himself sent a letter to Fulham last Friday in which he wrote: "Please also consider this letter from me to be an additional expression of sincere regret and apology from our club to your club for our actions last summer. Our club can do better and we pledge that it will."
Liverpool were keen on signing the 29-year-old in the summer with the club's owners, the Fenway Sports Group, announcing that they had recruited him from their Premier League rivals while he was on a break in the USA.
That was followed by Reds manager Brendan Rodgers heavily praising the USA international on Liverpool's official website and the club manufacturing shirts with Dempsey's name on the back.
Following Liverpool's apology, Fulham are now expected to drop their complaint to the Premier League about the Merseyside club unsettling Dempsey and eventually forcing them to sell him to Tottenham Hotspur.