Last year Suarez and Evra did not shake hands before a game at Old Trafford, just after the Uruguayan had served an eight game ban for using racist language towards the Frenchman.
Suarez denies that the language used was made with any racist intent.
Gerrard said: “I just think it’s time to move on. My advice to him [Suárez] would be to shake hands and move on. Suárez will make his own decision, of course he will. But I’d like to think he would want to move on himself.”
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.