Keane, who was overlooked by the club owners back in July when O'Driscoll was appointed, watched from the director's box while Forest handed out a St Stephen's Day hammering to Leeds United.
Sources suggest that the owners of the club were unaware he was at the City Ground until after the game.
A statement from Forest owners Abdulaziz Al Hasawi and Fawaz Al Hasawi said: "We are looking for an ambitious manager with Premier League experience.
"The timing of our decision may look a little odd after the win over Leeds, but sometimes you need to make changes with the long-term future in mind.
"Sometimes those changes need to be made from a position of strength rather than weakness and that is what we are trying to do."