Manchester United beat Liverpool 2-1 when the sides last met at Old Trafford last AugustLiverpool and Manchester United managers Jurgen Klopp and Erik ten Hag have called for an end to "tragedy chanting" in a joint statement.
The two sides meet at Anfield on Sunday and Ten Hag called their rivalry "one of the greatest in world football".
It has occasionally been marred by rival supporters chanting about the Munich air disaster and the Heysel and Hillsborough tragedies.
But Liverpool boss Klopp told fans to "keep the passion and lose the poison".
Ten Hag added: "It is unacceptable to use the loss of life - in relation to any tragedy - to score points, and it is time for it to stop."
Manchester United and Leeds United "strongly condemned" chants about historic tragedies when they met at Elland Road last month.
At the time, the Premier League said it is "treating the issue of tragedy chanting as a priority and as a matter of urgency".
Before this weekend's game at Liverpool, Ten Hag added: "We all love the passion of the fans when our teams meet, but there are lines that should not be crossed.
"Those responsible tarnish not only the reputation of our clubs but also, importantly, the reputation of themselves, the fans, and our great cities."
The Munich air disaster took place in February 1958, when a charter plane crashed, claiming the lives of 23 people, including eight Manchester United players and three officials.
In 1985, 39 fans died after being crushed against a wall which collapsed before the European Cup final between Liverpool and Juventus at Heysel Stadium in Brussels, while 97 supporters died as a result of a terrace crush at Liverpool's FA Cup semi-final against Nottingham Forest at Hillsborough in 1989.
"When the rivalry becomes too intense it can go to places that are not good for anyone and we do not need this," Klopp added.
"We do want the noise, we do want the occasion to be partisan and we do want the atmosphere to be electric. What we do not want is anything that goes beyond this and this applies especially to the kind of chants that have no place in football.
"If we can keep the passion and lose the poison, it will be so much better for everyone."
