Liverpool managing director Ian Ayre wants "rivalry not hatred" with Manchester United.
The Reds host United at Anfield in the FA Cup fourth round on Saturday.
It is the first time they have met since Luis Suarez was banned for eight matches for racially abusing Patrice Evra in the 1-1 draw in October.
Ayre said: "We mustn't detract from fans chanting and singing at each other but it needs to be a rivalry thing rather than a hatred thing."
There have been fears that the bitter relationship between the two sets of fans could reach new levels after the Suarez suspension, resulting in an ugly atmosphere at the match.
Following the ruling on Suarez, who will return from his ban at Old Trafford on 11 February, the Football Association called on the two clubs to get together to smooth relations before the cup tie.
United manager Sir Alex Ferguson, who insisted at the time that it was an unnecessary measure, has even written to the travelling fans,requesting that they behave at Anfield.
Despite his warning, Ferguson wants United's supporters to be "positive, witty and loud".
Ayre is also hoping that Saturday's clash produces a memorable football match in a lively atmosphere.
He told BBC Radio Merseyside: "It is the FA Cup, a great competition in English football and one we have a great history in and we want that to be what everyone focuses on.
"We have massive rivalry with Manchester United but those who are respectful also have respect for them because they are a great footballing side and team and, like us, they have been very successful.
"It is about a great spirit and a match between two great teams and it is certainly not hatred - there is no place for hatred in football.
"The banter on the terraces is great, both managers feel that as do the players. Far from trying to neutralise it we want our fans to be as vocal as they normally are against Manchester United.
"We definitely don't want to detract from that but both clubs have histories which have some things in people don't want to hear being sung about and so we want the fans to get behind the team, have a bit of fun and enjoy the game."