The clubs have a long history and a bitter rivalry both on and off the pitch.
But following this week's release of the Hillsborough Independent Panel's report - which cleared Liverpool supporters of any blame in the 1989 tragedy in which 96 supporters died - Ferguson is keen for a better relationship and more friendly rivalry to develop.
"We are two great clubs, ourselves and Liverpool," said Ferguson, ahead of Saturday's clash with Wigan.
"We should understand each others' problems. Maybe a line will be drawn in the sand in terms of their behavior towards each other."
The teams face each other next weekend at Anfield, and will be hoping for none of the controversy of last season.
Liverpool forward Luis Suarez was banned for eight matches after racially abusing Patrice Evra when the sides met last October at Anfield.
He then refused to shake the defender's hand before the game at Old Trafford in February this year, sparking an ill-tempered game which United won 2-1.
Meanwhile, Ferguson confirmed that Robin van Persie and Shinji Kagawa were fit and that Darren Fletcher, who has been plagued by a career-threatening chronic bowel condition, was also available.
"Darren Fletcher is in the squad, to give him a boost," said Ferguson. "At this moment in time everything looks fine."