Odds on the Cork native taking over at Parkhead were slashed on Thursday and the Republic of Ireland boss has admitted his assitant has been contacted by the club
Odds were slashed on Thursday on the former Manchester United captain taking over from the departed Neil Lennon at the helm of the Scottish champions.
And O'Neill - speaking in Keane's stead at a press conference on Thursday - admitted his assistant had been in contact.
"I had a call from Dermot Desmond asking me to talk to Roy [Keane] if it was possible," said O'Neill. "I mentioned it to Roy. I am sure there were talks, informal talks. I would be really disappointed if he leaves. But, it kind of felt when I took him on in the first place that over the course of two years, that this would happen.
"I did not think it would happen so quickly. He has had a number of offers from a number of football clubs. He has a lot to consider.
"Celtic are a very big club. Particular offers like this won't come around too often. It is a very big job, obviously."
Ireland head to London this weekend to face Italy in what will be their second of four end-of-season friendlies.
And while O'Neill is certain of the fact that Keane will be with the squad for the Italy clash at Craven Cottage, he cannot guarantee his presence in America where Ireland play Costa Rica and Portugal.
"He certainly would be involved on Saturday," said O'Neill. "Of course he will keep me informed the whole way through. We will take it step by step at the moment. Things can develop really quickly or really slowly. I would be disappointed if Roy does go, obviously."
Asked if he had any regrets in bringing Keane into the Ireland set-up, he said: "I have no regrets. Absolutely none, and he is not gone yet.
"We are at a very speculative time at the moment. I think with Roy coming into this job, we knew that these opportunities would come about. We will all be disappointed [if he leaves], the players, the backroom staff. Everyone."
Ireland play Italy at Craven Cottage in London on Saturday night with kick-off scheduled for 20:45 CET.