Owners Fenway Sports Group yesterday began the process of finding a successor for Kenny Dalglish after he was sacked on Wednesday.
While Ayre insisted no targets had yet been approached a short-list would be drawn up as quickly as possible based on the advice principal owner John Henry and chairman Tom Werner had gleaned from "pre-eminent people within football".
And while Dalglish was dismissed because poor league results in his first full season led to an eighth-placed finish, which FSG felt did not represent significant steps forward, his successor will not be judged immediately on results.
"The important thing will be to see progress and that means different things," Ayre said.
"Everyone will want to see that we believe we are going in the right direction and are moving up the table, achieving more, playing the right sort of football.
"As long as you believe week-to-week, month-to-month, season-to-season you are building on something then people will be given time.
"There is a difference between that and feeling you are not moving forward.
"The manager coming in has an interesting time because he has a new structure, a good foundation, a good squad of players and an opportunity to build on that with the support of owners, which is quite important.
"This ownership group has consistently supported, invested and stood behind the team."
Numerous names have already been linked with the vacancy and Ayre admitted he started receiving calls from interested managers just hours after Dalglish's departure was announced.
Reports claimed they had already started approaching targets - with former Porto and Chelsea boss Andre Villas-Boas named as one - but Ayre said the process only began yesterday [Thursday].
Former boss Rafael Benitez, out of work and living locally, is seen as an unlikely candidate.
Ayre said no-one was being ruled out at this stage but would not put a timescale on the recruitment process, although he admitted there were external pressures which meant there could not be too long a delay.
"Of course we will have a short-list very quickly. There are lots of names being bandied around and lots of people showing interest," he added.
"We will define what we are looking for and you shouldn't include or dismiss anyone on that basis.
"It will be as short or as long as it takes but it is impossible to say how long that will be.
"But we are going into a busy summer transfer window period and players will come back for pre-season so you want it in place to service that."
Scepticism has been expressed that the likes of Guardiola, Capello, Borussia Dortmund's Jurgen Klopp, Marseille's Didier Deschamps and former Porto and Chelsea boss Andre Villas-Boas would be interested in taking over at a club which will not have had Champions League involvement for three seasons.
However, Ayre believes the right candidate will see a bigger picture.
"We will find out (the effect of not being in the Champions League) during the process I guess," he said.
"The reason I don't think it will have an effect is if you lined up most managers in football and asked them if Liverpool would be a great club to manage and most people would aspire to do so I think they would say yes.
"The history of this club, the reach of this club around the world , its fanbase and everything we have achieved and want to achieve is more than enough to keep any manager we would want to go after hungry for the opportunity."