O'Neill enjoyed a successful five-year stint as Hoops manager between 2000 and 2005, winning seven trophies while also leading the team to the UEFA Cup final in Seville in 2003.
He dismissed the possibility of a taking charge for a second spell but insisted that Keane – his former Republic of Ireland assistant – could be the man to bring success back to Celtic.
Keane, currently a pundit with Sky Sports, has not managed in 11 years since ending a two-year spell in charge of Ipswich, having previously bossed Sunderland.
On his own Celtic prospects, O'Neill told Sky Sports: “I’ve had a great time here but my time is gone.
“The torch has been passed and it’s up to other people now.
"My own personal view is that owners and chief executives are missing a trick by not thinking about Roy as their manager.
“That is my view. He has learned a great deal and he is very capable of taking a top job.
“I am not party to what is going on but I do think there is time for Celtic.
“Callum McGregor mentioned it. They have to think of someone who will give them the chance to go and win again.
“Rangers are on the up at the moment. They haven’t been there for a long time - but who can get Celtic momentum again?
“That’s what they will be thinking about.”
O’Neill was speaking after taking in Celtic’s 1-1 draw with Rangers at Parkhead.
He added: "Celtic had enough chances to win the game but old frailties came up again - losing set-piece goals.
“They allowed Rangers to come back into a match they were dominating at that particular time.
“I felt the game fizzled out in the second half and a draw was maybe a fair result.
“In terms of build-up play, Celtic were fine but doing that is one thing, finishing it off is another matter.
“They haven’t been able to do it this season and this game was almost symptomatic of how they have been over the season.”