The former Anfield favourite admits that there is no love lost between the sets of supporters in a week where his fellow Scot has written a letter to the United fans to discourage them from singing abusive.
"When the Hillsborough disaster happened back in 1989, Sir Alex Ferguson was straight on the phone to offer his help in any way he could," Dalglish told the Daily Mirror.
"People out there have different opinions about him. Some love him, some hate him, but when something terrible happens, like Hillsborough, Alex is one of the first asking what he can do.
|10/1||Fabio Borini is 4/6 with PaddyPower to score first when Liverpool face Manchester United on Sunday
"So although there is an intense rivalry between Manchester United and Liverpool, it would never prevent Alex from offering his assistance, which is exactly what he did back then."
The 61-year-old acknowledges that the Red Devils have also been on the receiving end of abuse in the past from rival supporters over the Munich disaster that cost the lives of United players in 1958, and has called for an end to the "scandalous" chants.
He added: "These chants, on both sides, are absolutely scandalous.
"Unless they've actually been through something like that, they can have no comprehension of how difficult it is for the people involved and the families affected by these kind of tragedies.
"Although there is no love lost between United and Liverpool, there is an underlying respect for each other, even though at times it might be through gritted teeth.
"That's why I don’t think there will be a problem at Anfield tomorrow."
Dalglish also believes that Luis Suarez and Patrice Evra will put their differences to one side and shake hands before kick-off.
"Tomorrow, the stakes are too high to allow personal issues to cloud their judgement," he added.
"If you can’t shake hands with an opponent and show respect to 96 innocent football fans who died, then you've got a major problem with yourself."