Liverpool striker Luis Suarez has been banned for 10 games for biting Chelsea's Branislav Ivanovic.
Suarez issued an apology for his actions on Sunday night, saying: "I am deeply sorry for my inexcusable behaviour earlier today during our match against Chelsea.
"I have issued an apology and have tried to contact Branislav Ivanovic to speak to him personally. I apologise also to my manager, playing colleagues and everyone at Liverpool Football Club for letting them down."
Ayre, who postponed a trip to Australia to deal with the incident, has made it clear this week that Suarez will not be sold.
"It affects his future in the sense that we have to work with him on his discipline - but Luis is a very important player to the club," said Ayre.
"He's a very popular player with his team-mates. As we keep saying, he signed a new four-year contract last summer and we'd all love to see him here throughout that contract."
Suarez has also received the support of team-mate Jamie Carragher, who says Liverpool are doing the right thing by backing the Uruguayan.
"The way things are now being pitched is that Liverpool have got to do something about the rotten apple in their midst," said Carragher.
"It is as if Luis is the only player to have represented Liverpool who has ever been embroiled in controversy. That simply isn't the case.
"Every one of the players I mention regretted what happened and Luis is the same. More importantly, the club stood by every one of them."
PFA chief Gordon Taylor expressed his disappointment over the incident, adding: "His reputation for controversy continues to increase when he can be such a good player, one of the world's best, so it is a real dilemma now."