Ferencvaros coach and former Celtic striker Keane has been mentioned as a candidate for the Hoops job when O'Neill steps down at the end of the season.
"Why not?" said O’Neill when asked if Keane should be a candidate for the job. "Robbie has done really fine at Ferencvaros, so why shouldn’t he be?
"The football club should be looking at someone of that sort of calibre. I worked with Robbie for a couple of years when I was the Republic of Ireland manager. We could have done with him when he was 26 or 27, rather than the latter part of his career.
"Did he strike me as a future manager? That’s always hard to say. When I was a player at Nottingham Forest, for example, I am not sure I thought of management all that much.
"The point I am making is that you think someone will be a manager, and it doesn’t happen. Personally, I might have been the most unlikely player at Forest to become a manager.
"So I don’t know enough about Robbie as a person to say how he would manage a group of people in a dressing room, but he’s made a fair fist of it so far."