Former Celtic striker Dion Dublin has named Frank Lampard and Sean Dyche as potential successors to Martin O'Neill at Parkhead.
O'Neill, who returned to Celtic for a third spell during the summer, signed a one-year contract with the option of an additional year and has led the team to a promising start to the season.
With Celtic sitting top of the Premiership after winning their opening five league matches, the club is not under immediate pressure to consider future management.
However, Dublin believes that replacing O'Neill will be a significant challenge for the club. He told Reviant: "There isn't anyone who is perfect to replace Martin O'Neill, and that's the problem for Celtic.
"You'll only find the perfect person once they're at the club and have proven they can win everything and have done everything the way you'd want them to.
"That's the issue."
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Despite Celtic's continued success, Dublin believes that the size of the task will deter many candidates. He added: "A lot of people will look at Celtic and say: are you joking? It's a massive club and a massive job.
"They fear the size of the football club - they fear the expectations of the football club."
The former Aston Villa and Manchester United striker believes Coventry City boss Frank Lampard would not be intimidated by the challenge.
He said: "I want Frank Lampard to stay at Coventry City, but he's the kind of manager from the new generation who wouldn't be fazed by it."
Dublin also suggested former Burnley and Everton manager Sean Dyche could be a strong fit. "What's up with someone like Sean Dyche at Celtic?
"I think that might work perfectly for all parties once Martin decides to go and hang his boots up."
