The Bhoys have had a testing week having lost 3-1 to Molde last weekend, but bounced back with wins over Dundee Untied and Hearts.
The problem for manager Deila has been that he has faced two major disciplinary issues over the last seven day - the last thing he needs as pressure mounts on him.
Against Molde, playmaker Kris Commons stormed off the pitch upon being substituted, and had a touchline row with assistant boss John Collins in an extraordinary turn of events in Norway.
Then, earlier this week, left back Emilio Izaguirre and striker Nadir Ciftci were involved in a training-ground bust-up which left Izaguirre requiring stitches, with tensions rising in training.
Commons started for Celtic in the 5-0 win over Dundee United, and even scored twice as the playmaker appeared to have resolved matters with Deila and Collins, but former Rangers winger Neil McCann isn't so convinced that it was the right move from Deila.
Speaking to Sky Sports, the pundit stated that he wouldn't have had Commons near the squad never mind starting for Celtic, and pondered whether Deila buckled under pressure.
"The former Scotland international has been excluded from lots of Ronny's starting line-ups," said McCann. "For whatever reason, he's found himself out of the side and you have to say it can't be due to any lack of ability, so why has he not featured more? One suggestion has been he hasn't conformed to the new management's fitness requirements. Whether that's the case or not, the man who scored 31 goals and won the PFA Scotland Player of the Year prize in 2013/14 is undoubtedly a fans' favourite."
"Personally, I wouldn't have let Commons near the squad, never mind the starting line-up. I think the manager should have put out a clear message that such behaviour is unacceptable at Celtic FC. I'm sure they had enough in their squad to beat bottom-of-the-table Dundee United without him. Did Ronny buckle under the pressure then of leaving out a player who is popular with supporters, at a time when the fans are starting to ask questions of him or was he the bigger man by putting the team before himself? Something, it's worth noting, Kris should have done!" he added.
With Commons' quality in front of goal and when creating chances for his team-mates, it's certainly hard to leave him out, but he must also know that his actions have consequences - and some feel that by immediately starting the next game, Deila wasn't hard enough on the veteran midfielder.