Manchester United chief executive David Gill is expected to hold talks with Liverpool managing director Ian Ayre in an attempt to calm tensions between fans before the clubs meet in the Premier League next weekend.
The build-up to United's visit to Anfield on Sunday has been marred by anti-Liverpool chanting heard at Old Trafford during last Saturday's 4-0 victory over Wigan.
United fan groups were quick to state that the chant of "Always the victims, it's never your fault" was not related to the Hillsborough disaster, in which 96 Liverpool supporters died.
But the airing of the chant, days after an independent report into the 1989 tragedy cleared Liverpool fans of any blame and revealed a huge police cover-up, has caused concern at both clubs.
It is understood preliminary talks between the two took place following the publication of the Hillsborough Independent Panel's findings on Wednesday.
At this stage, no plans have been made for a minute's silence to be held on Sunday in memory of those who died in the FA Cup semi-final at Hillsborough.
The possibility of wreaths being laid by officials from both clubs is also yet to be fully discussed.
There are also fears over a potential flashpoint involving Patrice Evra and Luis Suarez after the latter snubbed the former during the pre-match handshakes in February.
The Uruguayan's actions followed his eight-match ban for racially abusing Evra, and it has been reported that, when Gill and Ayre meet ahead of this weekend's game, they will discuss how best to avoid further controversy.
After the publication of the Hillsborough Independent Panel's report, United manager Sir Alex Ferguson and his Liverpool counterpart Brendan Rodgers called for an end to the unsavoury chanting that has marred matches between the two clubs.
Chants about both Hillsborough and the 1958 Munich air disaster have been heard from a minority of fans.
A United spokesman reiterated Ferguson's appeal after the chanting at Saturday's match, saying: "The manager has made the club's position very clear on this matter. It is now up to the fans to respect that."
In a statement, the Manchester United Supporters' Trust played down the significance of the chanting.
Chief executive Duncan Drasdo said: "Following this week's developments and release of revelatory information on the Hillsborough tragedy, MUST wishes to make it absolutely clear that, just as we condemn chants mocking the Munich air disaster, we also condemn any chants relating to Hillsborough or indeed any other human tragedy.
"We did hear the usual anti-Liverpool chants at the match but we're pleased to say, despite some reports to the contrary, there was nothing that was specifically referencing Hillsborough."