The Reds' reputation has taken a battering in some quarters because of the way they handled their defence of Luis Suarez, who was banned for eight matches after being found guilty of racially abusing Patrice Evra.
Saturday lunchtime's tie of the round between two of the world's best-supported clubs is sure to attract a massive global audience and managing director Ayre thinks, in the light of recent criticism, they should use it to redress the balance.
"Everyone has a role to play, just as we have a role to play at the club," he said. "On Saturday it is about the fans representing Liverpool Football Club on the terraces, supporting the team and manager.
"It is not about some sort of hatred for Manchester United - we all have that passion and want to beat them but it starts and finishes there.
"The world will be watching and we want the world to know Liverpool is a great club with great supporters.
"There is a lot of attention on this game, in some ways for all the wrong reasons, and we should see that as an opportunity.
"There have been a lot of people with perceptions about Liverpool in the last month or so, making comments which are wrong, and what our fans, players and manager have a chance to do is put that right.
"We are a great club with a great set of supporters and that is what people should see."
Ayre stressed the focus should be on football and not the simmering animosity which has been fuelled by rivals fans' stance on Suarez and Evra.
Rumours abound about what will be worn, written and chanted at Anfield but Ayre said he hoped the usual rivalry could be maintained without people overstepping the mark with chants about the Munich air crash or the Hillsborough disaster.
"We have a massive rivalry with Manchester United but those who are respectful also have respect for them because they are a great footballing side and like us have been very successful," Ayre told BBC Radio Merseyside. "We mustn't detract from fans chanting and singing at each other but it needs to be a rivalry thing rather than a hatred thing.
"It is about a great spirit and a match-off between two great teams and it is certainly not hatred - there is no place for hatred in football."
Ayre added: "The banter on the terraces is great, both managers feel that as do the players.
"Far from trying to neutralise it we want our fans to be as vocal as they normally are against Manchester United.
"We definitely don't want to detract from that but both clubs have histories which have some things in people don't want to hear being sung about, and so we want the fans to get behind the team, have a bit of fun and enjoy the game."
