The Hoops are only on top of the Scottish Premiership on goal difference.
Former Celtic defender Marc Rieper has suggested that Ronny Deila has failed to capitalise on Rangers' absence from the Scottish Premiership by making very little progress during his time at the helm, the Daily Record reports.
The Norwegian took over at Parkhead in 2014 and won both the Premiership title and Scottish League Cup during his first season with the club. This season however, the Hoops were knocked out of the League Cup at the semi-final stage, fell at the play-off stage of the Champions League, and subsequently finished bottom and winless in their Europa League group.
While they remain in the Scottish Cup and are top of the league, Aberdeen are now level on points with Deila's men and arguably have some considerable momentum, having won the clash between the pair last week.
And Rieper - who made 37 league appearances for the club - believes that his former side should have done much better this season, before hinting that their inability to be dominant reflects badly on Deila's time at the club.
"In a league without Rangers then the margin should be much bigger than it is now and that is without taking anything away from Aberdeen who have been fantastic," he said, as reported by the Record.
"But if we are being really truthful then with the size of Celtic's budget and the players they have at their disposal then it's so much bigger than anything else in Scotland, apart from Rangers.
"The gap must be bigger. I can understand maybe one season to find your feet but you can’t go out of the Champions League three times in a row and finish bottom of your Europa League group. That is where any Celtic manager must be measured, especially now without Rangers."
With Rangers out of the picture, there is little question that the Bhoys should have taken the opportunity to establish themselves as the all-conquering side in the Scottish game.
And while they have collected two trophies during Deila's tenure, and are on course for potentially another two, their inability to get the title practically wrapped up by this point, as well as their struggles in Europe suggests that they have become complacent since their rivals were forced to make their way through the divisions.
With a game in hand over Aberdeen, and a much more superior goal difference, Celtic should still be the favourites to clinch the league crown. However, it will surely not be considered that great a success if it goes down to the wire and they have to do it in Helicopter Sunday style.