The pleas regarding chants and online abuse about events such as Munich, Heysel and Hillsborough were made in a joint statement issued by the clubs on Saturday, with Klopp urging fans to keep the passion and lose the poison.
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.
Ten Hag said: 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.
The statement concluded: Together, Liverpool and Manchester United want to show the special and positive side of this wonderful rivalry between two great football clubs with proud but, at times, tragic histories.
Last month the Premier League said it was treating the issue of tragedy chanting as a matter of urgency following Uniteds 2-0 win at Leeds on February 12.
The league joined both clubs in condemning chants heard during the match, with there having been songs about the 1958 Munich air disaster from a section of the home end along with some plane gestures and some of the away support chanting about the death of two Leeds fans in Istanbul in 2000.