Celtic chief executive Peter Lawwell has confirmed Roy Keane is one of the candidates for the managerial vacancy at the club.
The Scottish champions are currently looking for a replacement following Neil Lennon's decision to leave Celtic Park last week.
Lawwell stressed Celtic have over a handful of contenders on their shortlist, but insisted the board will not be rushed into making an appointment.
"Hopefully it won't take too long but I'm sure you'll understand there's not much more we can say when we're midway through that process," Lawwell told Sky Sports News.
"There are between five and 10 at the moment.
"Clearly we want to do it as soon as we possibly can, but with these things you can't put a timescale on it.
"You just have to do your work properly and hopefully we'll get there as soon as we can, but as soon as we do that we'll let our supporters know.
"I think we'd like to do it as soon as possible, but again you don't want to get it wrong by going too fast. You need to take your time and make sure you get the right guy."
Republic of Ireland boss Martin O'Neill revealed on Thursday that Celtic majority shareholder Dermot Desmond had been in touch to speak to his assistant Keane.
"Roy has a lot to consider," said O'Neill. "I had a call the other day from Dermot Desmond wanting to speak to Roy if it was at all possible, and I mentioned it to Roy, of course.
"I am sure he was wanting to have a chat anyway, because a club like Celtic might not come around too often.
"It was just a really informal chat, I think. Of course I would be really disappointed if Roy was to leave us."
When asked about the comments of the former Celtic manager, Lawwell was pragmatic on the issue.
"Well Martin, he's absolutely accurate," Lawwell added. "We have got a number of, what we think are excellent candidates. Roy is one of them, and we'll see what happens in the next week or two.
"Roy has played here, he's a Celtic supporter, he's a first-class guy and like the others are - like I say we've got between five and 10 - a lot of great candidates and we'll just wait and see."