Professional Football Association chairman Clarke Carlisle believes it is vital to try and help Patrice Evra and Luis Suarez sort out their differences after the feud escalated.
The pair came face to face on Saturday for the first time since Suarez served an eight-match suspension for being found guilty of racially abusing Evra during a Premier League match at Anfield in October.
However, the Liverpool striker's refusal to shake the hand of the Manchester United defender meant there was no chance of the row being brought to an end, and there were strong words from both managers after the final whistle as Sir Alex Ferguson branded Suarez 'a disgrace' and Kenny Dalglish turned his fury on the media after claiming not to have seen the incident.
PFA chief executive Gordon Taylor also admitted it was fair to say the Respect campaign had been destroyed in the wake of what happened at Old Trafford, and Carlisle feels the situation will now require some mediation.
Asked if the PFA would step in, Carlisle told Sky Sports News: "Yes, without doubt.
"There have been many attempts made by Gordon to get these two gentlemen into the same room in an attempt at mediation.
"It wasn't to be and the due process was followed to get a verdict in the original incident, but now after yesterday's incidents I'm sure that Gordon will be stepping up his attempts to try and get some sort of closure on this situation."
There have been suggestions that the pre-match handshake should now be scrapped in all matches to avoid similar controversy, with Wayne Bridge's snub of John Terry in 2010 also generating unwanted headlines for the PFA.
However, Carlisle insists it is an important part of the game and has called on players to set an example by showing they can leave private gripes aside and be professional.
"This has shown itself as a personal grievance yesterday between Luis Suarez and Patrice Evra, and that is the kind of situation we don't want transferring onto a football pitch," Carlisle explained.
"There has been a big debate about whether we should get rid of the handshakes altogether and I am adamant that we should keep them in the game because, personal grievance aside, when you cross that white line you should have an element of professional respect from one professional to another.
"That is what the handshake is all about, it is about respecting your opponents and respecting the referees and officials when you are in those 90 minutes, and we should be able to leave our personal grievances off the pitch because, when you bring them onto the pitch, that is when problems start.
"It has been a monumental success I feel in establishing that rapport between opponents and officials and these two incidents have highlighted how we need to further define the line between personal and professional relationships."
Carlisle admitted he was saddened by the scenes at Manchester United, saying that Suarez missed the opportunity to bring closure to the row.
"I was bitterly disappointed. The racism element of this incident made it a national topic and the intense rivalry between Manchester United and Liverpool also amplified the situation, so this was a real chance to defuse that tension and Luis didn't take that up.
"If anything he poured a bit of fuel on the fire and exacerbated the situation, and it was a shame to see that Kenny Dalglish seemed to have no inkling it had happened.
"Moving forward, we really need to get Patrice Evra and Luis Suarez together and try and have some kind of mediation so that when you step onto the pitch in front of the eyes of hundreds of millions of watching people, the impressionable young supporters that we set an example to, that you can put differences behind you when it comes to sport and a game of football."