Former Ireland international Keane has been linked with the managerial vacancy himself, but has seen O'Neill emerge as the clear favourite to land the post.
The Northern Irishman has vast coaching experience, with a distinguished career having taken in spells at Wycombe Wanderers, Norwich City, Leicester City, Celtic, Aston Villa and Sunderland.
He was relieved of his duties at the Stadium of Light in March, but could be tempted to step back into the dugout on the international stage.
Keane believes O'Neill is the ideal candidate, but has praised the Football Association of Ireland (FAI) for not rushing into an appointment and allowing caretaker boss Noel King to oversee two final 2014 World Cup qualifiers against Germany and Kazakhstan in October.
He told reporters at the Mayfield Community Volunteers Awards in Cork: "I know a little bit about Martin O'Neill and I think Martin would be a very, very good choice.
"I think the FAI have done the right thing in stepping back, taking their time and seeing what is out there.
"A lot of managers have been linked with it. A lot of good managers."
On the reports linking him with the job, Keane said: "I haven't been contacted by anyone.
"I have not thought about it too much to be honest with you. I have more important things to be worried about."