The Parkhead club's majority shareholder, Dermot Desmond, has made contact with Keane about taking over from Neil Lennon.
Keane, 42, would have to resign as O'Neill's assistant manager with the Republic of Ireland to take charge at Celtic and he has yet to declare how enthusiastic he is about taking the job. However, O'Neill spoke publicly about Desmond's approach at a pre-arranged press conference in Dublin late yesterday afternoon and it is inconceivable that he did so without Desmond's prior knowledge and approval. O'Neill appeared at the event as a late stand-in for Keane, who had been scheduled to face the media to preview Ireland's friendly with Italy tomorrow.
Keane must now deliberate over whether to become manager at the club where he had a brief spell at the end of his playing career, between leaving Manchester United and announcing his retirement in June 2006. He is expected to be in the Ireland dug-out when they face the Italians tomorrow evening.
O'Neill, who was Celtic manager between 2000 and 2005, made Keane his assistant when he got the Ireland job in November last year. Last night the manager said he would try to persuade Keane to stay.
"I'm going to do my very best. He is thinking things over," said O'Neill. "He has a number of things to think about, including a number of other offers as well. He has been great for the [Ireland] players and all round. I will be really disappointed [if he goes].
"He wouldn't take it [the Celtic job] lightly. He genuinely loves it here. It is great for him. He said it to me over the course of time that he loves it. I hate to use the word 'rehabilitation' here in the country but it has been really great for him.
"I have often said here that he will be a manager again himself. I just didn't expect it that quickly. It was only an informal conversation he was having. I don't know the ins and outs. I think they [Celtic] do have a list of people that they are speaking to. You never know, maybe they might speak to someone else."
O'Neill was sceptical when it was put to him that Keane could take the Celtic job and still remain involved with the Irish. "If you are a full-time manager at a club, I don't know whether it would work. If there was a way of keeping here, I would like to try and look at that as well."
Celtic's approach for Keane drew plenty of criticism on social media from supporters unconvinced by his previous managerial spells with Sunderland and Ipswich Town. O'Neill, though, said that he saw similarities between Keane and the man he may succeed.
"Neil Lennon I know as a player," he said. "I signed him twice and he was fantastic. I'm sure there were moments when he thought that management wasn't for him.
"Roy, as a manager, did great at Sunderland and he was disappointed with things at Ipswich. Essentially they are both managerial material."
Desmond would not show Keane the disrespect of making an approach for him only to offer the Celtic job to someone else, so the club's preferred choice is now obvious. Last night Celtic issued a brief statement: "The club can confirm that it is continuing discussions with a number of excellent candidates."
Earlier yesterday it was claimed that Celtic had offered the job to Dan Petrescu, the former Chelsea player who left Dynamo Moscow by mutual consent last month and is out of work. The 46-year-old, who was in charge of unfancied Romanian's Unirea Urziceni when they stunned Rangers 4-1 in the Champions League at Ibrox five years ago, had been contacted
by Celtic according to Dumitru Stangaciu, his long-term assistant manager.
"Dan is in negotiations with
a lot of clubs," Stangaciu said. "One proposal is from Celtic, there is also firm interest from China and other countries too."