The Scot was sacked on Wednesday just 12 months into a three-year contract after Fenway Sports Group determined an eighth-placed Premier League finish did not represent sufficient grounds for optimism.
Dalglish led the Anfield outfit to a first trophy in six years, the Carling Cup, and an appearance in the FA Cup final but it wasn't enough as the Americans left no room for sentimentality in removing the 61-year-old fan favourite.
Wigan manager Roberto Martinez, Swansea boss Brendan Rodgers, Andre Villas-Boas (who was sacked by Chelsea earlier this year) and NOW Alan Pardew are the four names already linked with the post.
Ayre told Liverpool's official website: "Whether it was the board of Liverpool recruiting Bill Shankly many years ago or the recruitment of Kenny Dalglish 18 months ago, it's the same process.
"The board will create a criteria of what that manager should look like and we'll match that with the best possible candidates and make a decision on that basis.
"That (the time frame) will be dictated by finding the right candidate of the right quality.
"What we want is the best, what we don't want is to choose quickly or choose because there's a time pressure. It'll be about finding the right person who can do the best job for Liverpool Football Club."
Sacked Liverpool manager Kenny Dalglish has given his backing to owners Fenway Sports Group.
The iconic Anfield figure had his contract terminated on Wednesday following a season which saw the club lift the Carling Cup and reach the FA Cup final, but endure their worst league points return since 1953/54.
Dalglish: "I would hope nobody would prejudge things now.
"The owners have their own reasons for doing what they have done.
"They came in to help the club at a time when it wasn't in a great condition.
"They have improved it, taken it forward and are doing the best they can.
"Liverpool is still a great football club, still a club that should believe in whoever is going to come in after myself.
"The supporters, not just for myself but for everyone else, have always been fantastically supportive of the team and that should not change."