Tensions are sure to be high at Old Trafford, as it will be the first meeting between the two sides since Suarez completed his ban for racially abusing Evra.
Concerns have been raised about how Suarez and Evra will react when coming eye-to-eye, but Reds boss Dalglish claims to have spoken to his player and expects him to honour the pre-game handshake.
"People are already speculating on the pre-match ceremony, but from Luis' point of view we have spoken to him and I know he will shake the hand of Patrice Evra and the other Manchester United players before the game," Dalglish told the club's official website.
Dalglish has called on all connected with both clubs to conduct themselves to the highest standards and feels the time has come to put the affair behind them.
He said: "Everyone involved, including the media, the supporters and both teams have a responsibility to ensure this weekend is remembered as a cracking game of football between two very good sides, rather than for anything else.
"I thought everyone involved in the FA Cup tie at Anfield played their part in making sure that the match was played in the right way, so let's make sure that happens again this weekend.
"I'm sure people will want to talk about Luis Suarez, but he accepted his ban, served his suspension and returned against Spurs on Monday. It's time for all of us to draw a line under what happened and move forward."