The call comes in the wake of the independent report into the Hillsborough disaster which was released this week. United fans have in the past taunted Liverpool fans about the disaster while Liverpool fans have responded with chants about the Munich disaster of 1958 in which a number of Manchester United players were killed.
“You’d hope that this is a line in the sand in terms of how the fans behave with one another,” Sir Alex said at a news conference today.
“We are two great clubs and we should understand each other’s problems in the past. Certainly the reputation of both clubs doesn’t deserve it.
“Both clubs have suffered fatalities through football.
“You hope that fans do behave themselves and support their team and that will be the end of it.
“The fact we are playing them after the findings we have been reading about in the last couple of days does bring a focus to it,” he added.
Liverpool’s first home game after the disaster’s findings were revealed will be against United a week on Sunday.
Sir Alex added that Darren Fletcher will be in the United squad to face Wigan Athletic at Old Trafford tomorrow. The midfielder has missed the last ten months with a bowel complaint.
“Darren’s training well and played in the reserves on Tuesday night,” said Sir Alex.
“The next step is when we can involve him in a game in the first team. He’s in the squad tomorrow, simply because I think it will give him a boost. It’s a chance to progress.
“At this moment in time everything’s going fine for him. We understand the condition he has to deal with – that can change but hopefully he’s managed to conquer it in terms of his diet and how he handles it. Things are going well at the moment.”
Shinji Kagawa and Robin van Persie are also in the squad despite injuries picked up in their respective midweek World Cup qualifiers and both are expected to play against Wigan.
Meanwhile, United are to erect a 9ft (3m) statue of Sir Alex outside Old Trafford. The statue will be created by sculptor Philip Jackson and will be placed in front of the North Stand, which was renamed the Sir Alex Ferguson stand to mark his 25 years in charge of the club.
“I have met Sir Alex on a number of occasions and he is a very nice chap,” said Mr Jackson.
“I took a lot of pictures of him and watched a lot film. You have to get to know the subject.
“He came down to see the clay sculpture and he seemed very pleased.”