Suarez last season refused to shake Evra's hand after being banned for eight games for racially abusing the United defender, but Gerrard will intervene this time around.
Gerrard admitted: "I think that Luis and Patrice could be the key.
"That's going to be at the beginning of the game - the handshake - and if it goes ahead, then they've got a responsibility to start the day off on a good note.
"I will speak to Luis. I just think it's time to move on.
"My advice to him would be to shake hands and then move on.
"Luis will make his own decision, of course he will.
"But I would like to think that he would want to move on himself and put it to bed."