Next month's meeting at Old Trafford has become a focal point as it is likely to be Luis Suarez's first away from Anfield following the end of his eight-match suspension for racially abusing United's Patrice Evra.
Despite their rivalry on the pitch the two north-west clubs have enjoyed cordial relations off it in recent years, but those have been strained during the three-month investigation and subsequent punishment of Suarez.
However, Press Association Sport understands the Merseysiders are keen to rebuild bridges now they and the Uruguay international have accepted the punishment.
They will start with their arch-rivals with talks likely between top executives, although the club have not ruled out the possibility of discussions taking place between American owners John Henry, who also heads up the Boston Red Sox baseball franchise, and Malcolm Glazer, who owns NFL side Tampa Bay Buccaneers.
A spokesman for Henry declined to comment on the Suarez matter, choosing instead to stand behind the club's lengthy statement on Tuesday evening in which Liverpool criticised the Football Association for constructing "a highly subjective case against Luis Suarez based on an accusation that was ultimately unsubstantiated".
While attempting to re-establish their previously positive relationship with United, Liverpool will also continue dialogue with the FA as they seek to smooth over cracks which appeared during the fractious period once Evra made his allegations in mid-September.
Liverpool were unhappy with the manner of the investigation and believe the process is flawed.
Their statement in midweek said: "The FA and the panel chose to consistently and methodically accept and embrace arguments leading to a set of conclusions that found Mr Suarez to 'probably' be guilty while in the same manner deciding to completely dismiss the testimony that countered their overall suppositions."
However, in the wake of Suarez issuing an apology - though not to Evra - for any offence his use of the word "negro" may have caused, Liverpool want to now draw a line under the matter.
They are keen, though, for some progress to be made in cutting down on the offensive chants which the striker has had to endure since the allegations arose.
Suarez is likely to face the severest of treatment at Old Trafford - which would be his second match back after suspension if Liverpool beat Oldham in the FA Cup tonight.
In the intervening period his club will do all they can to lessen that impact but manager Kenny Dalglish has no qualms about selecting him for that match.
"I will be delighted to get him back," said the Scot when asked whether he would consider playing the striker against their fiercest rivals next month.