The Republic of Ireland assistant manager has been linked with a move to the Scottish Premiership club.
Martin O'Neill has insisted that he would have no problem if Roy Keane wanted to leave the Republic of Ireland to take the Celtic job, and suggested that the retired midfielder would be a success at Parkhead, The Scottish Sun reports.
The Hoops will be looking for a new manager at the end of the season, and their former midfielder appears to be one of the favourites to succeed Ronny Deila.
And while O'Neill claimed that his assistant had not been approached about the role as far as he was aware, he suggested that he would expect Keane to do well with the Scottish Premiership side if he ultimately took the position.
"I think Celtic is one of the great clubs in the world and I have to say that he was one of the great players in the world, so that's not a bad fit for a start," he told The Scottish Sun.
"Could he do the job? I would have no problems with that whatsoever. Would he be capable of doing that? Absolutely.
"But as Roy said, you still have to be asked and so far, I'm not so sure that that's been the case."
While the Irishman's managerial career has not been spectacular so far, he not only has an understanding of the expectation at a club like Celtic, having spent time with the Bhoys during his playing career, but the amount of success he enjoyed as a player - including in the Champions League - should help him instil that winning mentality into the squad.
And having spent the last couple of years working closely with O'Neill - who won plenty of trophies during his time in charge at Celtic Park, and led the side to the UEFA Cup final - he may have no problem leading the club to next level.