O'Neill's 42-year-old assistant has been heavily linked with the post vacated by Neil Lennon last week.
O'Neill told Irish journalists that Keane held talks with Celtic's majority shareholder Dermot Desmond about the position but said that it was still at the speculation stage and that he hoped Keane would remain with the national team.
"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."
Former Manchester United and Ireland captain Keane had mixed managerial spells at Sunderland and Ipswich.
Keane was a Celtic supporter as a boy and enjoyed a brief six month spell at the club at the end of his career before being forced to retire due to injuries.
Celtic have since released a statement on the club website, confirming that the club was still in the process of searching for a new manager.
The statement read: "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.”
- Sports & Recreation
- Dermot Desmond