The chief executive of the Professional Footballers Association has called for Luis Suarez and Patrice Evra to shake hands this weekend.
"I would hope that would take place, that would be a sign that having gone through the situation that those two players would shake hands and we can move on," Taylor told Sky Sports News.
"If they can accept that having paid that penalty, like Suarez has, that you learn from it and move on.
"That is the only chance we have got, if we can do that."
Suarez returned from his eight-game ban for racially abusing the United defender in Liverpool's 0-0 draw with Tottenham Hotspur on Monday.