Sir Alex Ferguson expects Manchester United's Premier League visit to Liverpool on Sunday, September 23, to pass off without a problem.
Ferguson has called for an end to the hostile rivalry between the two clubs.
Encounters between England's two most successful teams have become increasingly tense in recent times.
Last season was particularly bad, with Luis Suarez eventually being found to have racially abused Patrice Evra at Anfield, then failing to shake the defender's hand during the Old Trafford return.
Supporters have wasted no effort in trying to goad their opponents with particularly vile chants about Hillsborough and Munich, paying scant respect to the 96 Liverpool fans who died in Sheffield or the 21 who were killed coming back from a European Cup tie in Belgrade 31 years earlier.
However, in the wake of this week's Hillsborough Independent Panel's report which cleared Liverpool supporters of any blame in the 1989 tragedy, a chance exists for some of the edges to be taken off a rivalry that will always exist due to the nature of the two clubs.
Ferguson certainly hopes so and, with the eyes of a nation on them next Sunday, the Scot feels tempers will remain in check.
"There is such a focus on it at the moment that fans will be on their best behaviour," he said.
"It is a moment for those two great clubs to show why they are great clubs and I don't anticipate any problems.
"Both clubs have suffered fatalities through football and the fact we are playing them after the findings we have been reading about over the last couple of days does bring a focus to it.
"You would hope that maybe this is a line in the sand in terms of how the supporters behave with one another."
Ferguson had been manager of United less than three years when Hillsborough occurred.
Indeed, it was his team being beaten in the quarter-final by Nottingham Forest that set up that fateful Liverpool semi-final in the first place.
It was a very different age and Ferguson recalls incidents which seemed innocent enough at the time, but could have had equally catastrophic consequences.
"The thing that always sticks out in my mind at that time were the fences around the stadiums," he said.
"I remember us going to Derby at the time of Michael Knighton and they had fences around the grounds.
"We took a massive support. Michael Knighton was walking around shaking hands with the fans and they were trying to climb over the fences. It was frightening.
"You think back to those days with the fences. They were put up to avoid fans going on to the pitch.
"It was a period when there was fan behaviour throughout the country but it turned out to cost people lives because I think it contributed to what happened at Hillsborough."