Celtic insist they are considering "a number of excellent candidates" after Martin O'Neill claimed his Republic of Ireland assistant Roy Keane has held informal talks with the Scottish champions.
The Hoops are searching for Neil Lennon's replacement and Ireland boss O'Neill, who spent five years in charge at Parkhead, confirmed on Thursday that Keane had spoken to Celtic owner and majority shareholder Dermot Desmond.
But while O'Neill is bracing himself for the possible departure of his 42-year-old assistant, Celtic made it clear the recruitment process is still ongoing.
A statement released on Thursday said: "Following speculation concerning the manager's position at Celtic, the club can confirm that it is currently continuing its discussions with a number of excellent candidates.
"We will continue this process and select who we regard as the best appointment for Celtic. We will update our supporters as soon as this process is complete."
Another former Celtic player, Swedish striker Henrik Larsson, had preceded Keane as the bookmakers' favourite, alongside Owen Coyle.
Speaking ahead of Ireland's international friendly against Italy, O'Neill had said: "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 chat anyway because a club like Celtic might not come around too often.
"It was just a really informal chat, I think, but if you are asking me would I be really disappointed? Of course, if Roy was to leave us."
Keane, who played 10 times for Celtic before retiring in June 2006, linked up with O'Neill last November when the 62-year-old Ulsterman accepted the challenge of replacing Giovanni Trapattoni.
O'Neill added: "I only reiterate what I said right at the beginning, which I think has been enhanced over this last period of time.
"Roy has been, selfishly, he's been great for me. I've genuinely enjoyed working with him.
"He's sometimes a totally different character to the one that you see on the TV. He's been excellent, the players have enjoyed him immensely.
"I can only say that naturally I'd be disappointed if he left because I really think that he's been terrific.
"We have only had four games with the squad, but he's been excellent and I don't think that he'd give that up lightly."
Questioned as to whether or not the former Sunderland and Ipswich boss was ready for the task of managing the Scottish champions, O'Neill replied: "I think Roy's ready for anything. I think he's always been ready for anything."