Ronny Deila is in charge of Celtic at the moment, but he will leave the Scottish Premiership giants at the end of the season.
Keane is a former Celtic player, and the ex-Republic of Ireland international midfielder has managerial experience in club football with Sunderland and Ipswich Town.
Former Hibernian and Heart of Midlothian midfielder Stewart believes that the ex-Nottingham Forest midfielder would be a good managerial appointment for the Glasgow giants.
“Potentially, Roy could be absolutely dynamite for them,” Stewart wrote in The Scottish Sun. “I remember him starting at Sunderland and they were soon on fire — the place jumping and promotion to the Premier League quickly achieved. I could see him making the same instant impact with Celtic.”
“Major shareholder Desmond and chief executive Peter Lawwell surely know the club desperately needs a lift with their next appointment,” added the former Scotland international.
“They need a manager of real stature who can inspire and galvanise everyone. Roy unquestionably would fit the bill — and he’d also provide a huge commercial benefit, given his profile as one of the biggest names in world football.”
Keane is one of the greatest footballers in football history, but his managerial record is not that brilliant.
A key problem that the former United star could face at Celtic is the limited talent and quality of the players.
True, the Bhoys have the strongest team in Scotland, but how many of the players would be able to play for a mid-table Premier League side?