The Celtic legend feels that the club are going backwards under the Norwegian.
David Provan has told the Scottish Sun that Ronny Deila is on borrowed time as Celtic manager.
Deila's side lead the way in the Scottish Premiership, but Aberdeen - four points behind - are breathing down their necks as Derek McInnes's boys threaten what would be a huge upset.
The Dons have come a long way in McInnes's three-year spell at Pittordrie, and they managed a 2-1 win over the reigning league champions just last month.
In contrast, Deila has struggled in his efforts to move Celtic forward, with the Bhoys competing in the Europa League for the last two seasons after being eliminated from Champions League qualifying.
With the Norwegian coach now making hard work of winning the league title, Provan feels it is time for the club's hierarchy to replace him with somebody like McInnes, whom he says would be in the reckoning if not for a five-year stint with Rangers during his playing days.
"The only reason the Dons are still on Ronny Deila’s shoulder is they have a better manager," Celtic legend Provan said in the Scottish Sun.
"Derek McInnes’ improvement of Aberdeen demonstrates the importance of putting the right man in the dugout. But for a five-year stint wearing Rangers colours, you can bet that McInnes would be in the frame to replace Deila right now.
"Make no mistake, the Norwegian’s time is up."
The writing could be on the wall for the 40-year-old if Celtic are eliminated from the Scottish Cup by Rangers after the Old Firm enemies were paired together in the semi-finals on Sunday.
The Bhoys are back in action on Saturday with a trip to Partick Thistle.