Celtic chief executive Peter Lawwell says the club has a shortlist of "five to ten" candidates for the manager's job.
The Scottish champions' majority shareholder Dermot Desmond has held informal talks with Republic of Ireland assistant boss Roy Keane.
Lawwell confirmed the 42-year-old is one of the names on the list but insisted he has not been offered the position to replace Neil Lennon, who quit last week.
Asked how many names were in the frame, Lawwell told STV: "Between five and ten.
"We are looking at a number of exceptional candidates and we're going through a process. Hopefully it won't take too long."
On a time frame for naming a new boss, Lawwell added: "Clearly we want to do it as soon as we possibly can but these things you can't put a time on.
"Roy is one of them and we'll see what happens in the next week or two.
"You just have to do your work properly and hopefully we'll get it done as soon as we can.
"As soon as we do that we will let our supporters know.
"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."