But there is no question of him being offloaded in the summer despite worldwide condemnation of his inexplicable actions in yesterday's 2-2 draw at Anfield.
"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," Ayre told liverpoolfc.com.
"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.
"He's a fantastic player, top scorer and everything we'd want in a striker, so there's no change there.
"This is more about getting him back on the right track and it's largely down to (manager) Brendan (Rodgers) now to work with him on that side of his character."
After yesterday's match Rodgers said discussions about what action to take over Suarez would involve owners Fenway Sports Group.
Ayre confirmed they had taken place and FSG fully backed the decisions taken.
"With any incident like this, any major incident at the club, we're in direct dialogue with the owners, always," he added.
"I spoke to them last night and they were happy with the way we were handling the matter.
"I think the most important thing is that we acted swiftly yesterday.
"Luis issued his apology and then we spoke with him last night and then again this morning."
But Ayre stressed the issue would not end there with Rodgers, who has a close relationship with Suarez, determined to tackle the player's ill-discipline.
"We've taken action to fine Luis for his actions," he said.
"Brendan has spoken to him and I've spoken to him and Brendan will be working with him further on his discipline.
"We'll work with Luis - Brendan particularly - on this side of his character in his game.
"Hopefully that puts the matter to rest from our point of view and we'll wait and see if there's any further action from the football authorities.
"You can see when you speak to him how sorry he is about it and he's certainly shown quite a lot of contrition to us - and as part of that, he's also asked we donate the fine to the Hillsborough Family Support Group.
"I think he felt like he let a lot of people down yesterday."
Suarez will be offered anger management counselling by the Professional Footballers' Association but it seems more likely Liverpool would be inclined to chose to utilise the services of their own in-house sports psychologist Dr Steve Peters.
He has been working one day a week at the club's Melwood training ground for most of the season, having enjoyed success most notably with Great Britain's Olympic gold medal-winning cyclists like Sir Chris Hoy and Victoria Pendleton.
Former Liverpool striker Craig Bellamy has also credited Peters with helping him change his behaviour for the better.
PFA chief executive Gordon Taylor said the players' union would offer the striker help to deal with his temper.
Taylor told Press Association Sport: "There is no doubting his football ability, that's why it is so disappointing and embarrassing when he lets himself down.
"We have to work hard on anger management now. We have trained counsellors in this field and we will be offering their services to Liverpool and the player to try to improve matters."
The Football Association is reviewing the incident and Suarez is likely to be charged later today and could face a lengthy ban.
Suarez apologised to Ivanovic in a phone call last night and this morning revealed he had been fined by the club.
"For my unacceptable behaviour yesterday the club has fined me today," the 26-year-old wrote on Twitter.
"I have asked the club to donate the money to the Hillsborough Family Support Group for the inconvenience I have created to the Liverpool fans and to Ivanovic."
It is understood Ivanovic was spoken to by Surrey Police at the club's Cobham training ground last night after complaints made to Merseyside Police were passed on to their southern colleagues, who wanted to ascertain whether the defender had sustained any injury.
That was found not to be the case and Ivanovic told police he did not want to press charges.
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