Jurgen Klopp and Erik ten Hag have released a joint statement to urge Liverpool and Manchester United fans to stop "tragedy chanting" ahead of their meeting at Anfield on Sunday.
Liverpool supporters have been asked to stop singing about the 1958 Munich air crash while United fans have been told to refrain from chanting about the 1989 Hillsborough Stadium disaster and the 1985 Heysel disaster.
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Both sets of supporters have been condemned for chanting about the tragedies in the past.
Liverpool manager Klopp said: "One of the main reasons why the rivalry between Liverpool and Manchester United is so special is that it is so intense and no one should ever want to change this.
"But at the same time when the rivalry becomes too intense it can go to places that are not good for anyone and we do not need this. 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."
The Munich air crash resulted in 23 casualties including eight members of the United team returning from a European Cup match in Belgrade. Moreover, the Hillsborough disaster in 1989 cost the lives of 97 Liverpool fans who were attending an FA Cup semifinal against Nottingham Forest.
Ten Hag said in the statement: "The rivalry between Manchester United and Liverpool is one of the greatest in world football. We all love the passion of the fans when our teams meet, but there are lines that should not be crossed.
"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.
"Those responsible tarnish not only the reputation of our clubs but also, importantly, the reputation of themselves, the fans, and our great cities.
"On behalf of myself, our players, and our staff, we ask our fans to focus on supporting the team on Sunday, and representing our club in the right way."