Former Celtic midfielder Stiliyan Petrov has warned the Hoops' managerial candidates there is no time for a lengthy rebuild of the Parkhead squad.
Eddie Howe, Roy Keane and Manchester City reserve boss Enzo Maresca remain the frontrunners to replace Neil Lennon.
But whoever takes over is likely to face a massive overhaul, with a number of new signings likely to be required to pick up the pieces of this season's shattered 10-in-a-row dreams.
However, Petrov insists the requirement to build a new team almost from scratch is an excuse the Celtic supporters are unlikely to accept.
The 41-year-old – who won four league titles, three Scottish Cups and another three League Cups with the Hoops – believes the fans will expect their team to mount a rapid assault to retake the Scottish Premiership prize after seeing it wrestled from their grasp by Rangers following a decade of dominance.
The retired Bulgarian told the Celtic Huddle podcast: "I'm sorry to say this but I don't think you can be a Celtic manager and say this is a rebuilding project. There's no such thing.
"I came from a foreign country and I had to learn very quickly and understand the DNA of the club, the demands of the fans.
"When you are the manager, you don't have time to do that, especially in today's football industry. You don't have time to rebuild.
"If you manage a club like Celtic, you have to win. You have to win as much as you can.
"If you don't, you'll lose your job.
"This is a job where people have to go in expecting to win. It's not a rebuilding process. There's no rebuilding time.
"That's unfortunately the reality but you have to face it."
Former Borussia Dortmund boss Lucien Favre and Arsenal great Thierry Henry are also among those to have be touted as Lennon's successor in recent days.
Keane – who starred alongside Petrov in the Celtic midfield for six months in 2006 after leaving Manchester United – and ex-Bournemouth boss Howe remain the favourites in Petrov's eyes.
But he would not be surprised to see other big names take an interest in the Parkhead post.
"Roy Keane and Eddie Howe are two very strong candidates, two candidates who can provide a lot to the Celtic fans," he said. "Both of them are completely different.
"Roy is fearless. We had the chance to play with him, we know how fearless he is.
"He is strongly opinionated. He knows what Celtic means and what the demands are.
"Eddie Howe has done a great job down in England and has had a tremendous amount of success with (Bournemouth). Everyone talks so highly of him.
"So I think it's two candidates with a very strong possibility to take Celtic to the next level.
"There are so many strong candidates. I'm not surprised. Celtic is a big club and everybody wants to be part of Celtic because of the fans, the culture, the history.
"I won't be surprised if it's an outsider who becomes the favourite again.
"If you're a manager looking to progress your career then Celtic is definitely a club you'll want to manage and to succeed.
"Whoever the manager ends up being, whether it be Roy, Eddie Howe, Thierry Henry, they should be looking forward to that. They should be excited to get the job and go toe-to-toe with Steven Gerrard and Rangers after what happened last season."
