Former Man United boss David Moyes said that Celtic is a "great football club" last night, but was reluctant to put his name forward for soon-to-be-vacant manager's job until the summer.
The club confirmed this week that Ronny Deila will leave at the end of the season.
Days of increasing speculation about the Norwegian's future, following the penalty shoot-out defeat to Old Firm rivals Rangers in Sunday's William Hill Scottish Cup semi-final, led to a statement being released on Celtic's official website which revealed Deila was to depart.
Moyes, who was installed by bookmakers as favourite for the job, was complimentary but non-committal when asked about the impending vacancy.
The former Everton manager told Sky Sports: "Celtic's a brilliant football club, a great football club, with unbelievable support and fan base.
"I'm going to wait until summer time and make a decision in the summer time.
"There's lots of clubs that will interest me and Celtic are a great club."
Hibernian boss Alan Stubbs was touted as a possible future Hoops boss earlier this season.
That was at a time when the Easter Road side were considered real contenders for the Ladbrokes Championship crown but they eventually fell away, leaving Rangers to clinch the title while Hibs now have a scrap on their hands to gain promotion through the play-offs.
But asked if he would be interested in swapping the green and white of Leith for that of Glasgow, Stubbs said: "I don't think it's a relevant question to be honest to be asking right now.
"I am more inclined to answer the question by saying that I'm just really sorry for Ronny. He seems a really good guy. I have spoken to him on a few occasions.
"I am disappointed for him more than anything and that is all I will say on the matter because I think you have to show a bit of respect.
"I have got a lot of things to think about between now and May 24 that are going to keep my mind occupied."
Republic of Ireland assistant Roy Keane and fellow Parkhead old boy Malky Mackay are also in the running.
Former Bolton boss Owen Coyle, long-serving Celtic striker Henrik Larsson and former Liverpool boss Brendan Rodgers are among others being quoted by the bookmakers, as is former Celtic manager Neil Lennon, who certainly wasn't coy in admitting his interest.
The Northern Irishman won three Premiership titles and two Scottish Cups and took Celtic into the Champions League during his four years as Hoops manager before leaving in 2014.
Speaking at The John Hartson Foundation charity golf day at Mar Hall, on the outskirts of Glasgow, the former Celtic midfielder, just out of an unsuccessful 17-month stint as Bolton boss, was asked if he would be interested in going back to Celtic Park.
"Absolutely," he said. "I would definitely be interested.
"I am not promoting myself for it but you asked me an honest question and I am giving you an honest answer.
"I think they will have someone in mind and there will be a long list of candidates for the job now because it is still a very attractive job for anyone.
"I was associated with the club for 15 years, I missed it when I left as a player and there are aspects you miss even now at 44 years of age."