The Republic of Ireland assistant boss has been linked with a return to the Scottish Premiership side.
Departing Celtic boss Ronny Deila has suggested that Roy Keane appears to have several of the attributes that the Hoops should be looking for when deciding on his successor at Parkhead, the Daily Mail reports.
The Norwegian is set to take charge of the Bhoys for the final time on Sunday before stepping down. And with speculation persisting as to who will be the person that comes in to replace him, Deila has suggested that the Republic of Ireland assistant may be a great option for the club.
"So much of managing in this job is about personality because you need to be a figurehead, too. You need a strong personality. [Keane] will handle all that pressure, to be a very good leader," he told the Mail.
"Also, I think it's important in this kind of job to have experience. It makes things easier. Having said that, there aren't many places you get experiences like this. If the new manager will call, I'll tell him what I think about things and help him if I can.
"But Roy Keane is Irish, of course. He has played at Celtic, he knows what the club's about, so he has a skill-set that could be good in the job."
Though Keane's only real success as a manager came during his time in charge of Sunderland, and thus, it would undoubtedly be the kind of gamble that the club may want to avoid after Deila's tenure, his leadership qualities may be what the side needs as they prepare for one of the most competitive league campaigns in recent years.
The retired midfielder led Manchester United to several trophies, including the treble in 1999, and it was often his demands of perfection that dragged the side to success.
With Celtic assuming a similar role to the one that the Red Devils enjoyed during that period, it could be his experience of leading a side with tremendous expectations that helps him finally prove that he can be as great as a manager as he was a player.