Celtic are looking for a new manager to succeed Ronny Deila at the end of the season.
Keane, a former Celtic player who won the Premier League title seven times and the Champions League once with United, is currently working as the Republic of Ireland assistant manager.
The former Nottingham Forest midfielder has club football management experience with Sunderland and Ipswich Town.
The former Republic of Ireland international is one of the greatest players in Premier League history, but his managerial record is not great.
A key problem that the former United star could face at Celtic is the limited talent and quality of the players.
Would Keane be able to work with players who are not at his level and have limited talent?
It would be best for Celtic if they look at someone proven and experienced, such as David Moyes, as Ronny Deila’s successor.