Former Celtic striker Sutton, who has been a leading critic of Deila’s management, insists even Rangers boss Mark Warburton would accept the Parkhead club still boast a higher standard of player in their team.
Based on current form of the Old Firm sides, Sutton believes Rangers could pose a genuine threat to Celtic in the Scottish Cup semi-final if the tie was being played this week.
But he also expects the Celtic players to “sober up” and regain an optimum level of performance in time to overcome their old rivals when the match does take place at Hampden on 16 or 17 April.
“It’s fair to say Rangers have a chance in a one-off game,” said Sutton. “But I do think Celtic are far, far stronger player-wise. I don’t think there is any doubt about that.
“How many of the Rangers players would get in the Celtic team? You have to look at form but all things being equal, if you asked Mark Warburton if he’d take the majority of the Celtic team over his team, then we’d all say yes he would.
“You have to give credit to Rangers this season but, having said that, they are in a league below Celtic which you would expect them to win and win well.
“You need to give Rangers credit for the way they performed in beating Dundee 4-0 last Saturday, on the back of Celtic drawing 0-0 against Dundee. You get all the hysteria on the back of those results - but don’t forget Celtic thumped Dundee 6-0 earlier in the season.
“The way I look at it, if I was a Celtic player right now I would be looking at the next five or six weeks before the semi-final as a chance for them to sober up, lift themselves and get themselves going.
“If Celtic were to meet Rangers today or tomorrow I think Rangers would be a worry for Celtic. But there is so much time before the game, where things can change.
“If the likes of Kris Commons, Scott Brown and Leigh Griffiths get their act together, then I still think a good Rangers. That’s the way it is and I’m sure both managers would agree.
“I wouldn’t say too much in the build-up to the game if I was a Celtic player or the manager. Privately, and this would go for Rangers as well, they will want to ram victory down the other team’s throat. It’s the way it is and always has been, there’s no point pretending otherwise.”
In a thus-far underwhelming season which has seen his team flop in Europe and exit the League Cup against Ross County in the semi-finals, Deila still has the opportunity to win the domestic double of Premiership title and Scottish Cup.
Sutton, however, remains unconvinced that even that achievement would be sufficient to restore the Norwegian’s credibility as Celtic manager.
“I’m not sure beating Rangers would make up for anything,” added Sutton. “A win would give him the chance of a double but I don’t know if things have gone too far for him.
“I look at Europe as the benchmark and I just think Celtic have regressed and have problems. Is it beyond redemption, even if they win the double? It depends on your definition of redemption.
“The fact less than 15,000 turned up for the game against Morton on Sunday, while other attendances have been iffy to say the least, tells its own story.
“Will Celtic win the league? Yes. Have they made it hard for themselves? Most definitely. It’s just that they have regressed and will find it difficult to qualify for any European competition next season.
“I don’t know what the board are thinking with respect to whether Ronny is still going to be manager next season or not. But the decision-making at the club has surprised me - there have been a lot of things I haven’t found logical or been able to understand this season.
“If Celtic were going to change manager, why not give him a transfer window to shop in? If they change in the summer, it won’t give the new manager a lot of time. The worry for me is that I just don’t see how this Celtic team can compete in Europe on the basis of the level of football they are currently playing.”