The Hoops have endured a miserable season so far, and are currently 23 points behind Scottish Premiership leaders Rangers with any hopes winning a 10th consecutive title all but extinguished.
Parkhead chiefs conducted little in the way of transfer business last month the remedy the situation either.
Jonjoe Kenny was the only senior addition to Neil Lennon’s squad in January, joining on a loan deal from Everton, while Olivier Ntcham and Jeremie Frimpong both sealed exits from the Glaswegian giants.
By contrast, Rangers completed deals for Aberdeen winger Scott Wright, as well as Bournemouth duo Jack Simpson and Nnamdi Ofoborh. The latter will join the club at the end of the season.
And Sutton is of the opinion that a complete overhaul could be needed at Parkhead if the Bhoys are to keep pace with Steven Gerrard’s rampant Gers.
Writing in a column for the Daily Record, he said: “Celtic need to start moving and there needs to be confirmed thinking. You have to have hope there is a major plan behind the scenes.
“Maybe it’s all in hand and the grand re-design will be unleashed in the spring.
“If there’s not, it’s a huge problem because, for a start, that dressing room needs ripped apart.
“Some of the chat after Olivier Ntcham’s move to Marseille summed it up. Neil said he was fed up. Frimpong couldn’t get out of the door fast enough.
“There will be others.
“The loan players will all likely return to the parent clubs. Mohamed Elyounoussi, Shane Duffy, Kenny and Diego Laxalt are in that boat.
“Also, there is a likelihood that Odsonne Edouard and Kristoffer Ajer are going to get big-money interest.
“Scott Brown is not getting any younger and there is going to be interest in Ryan Christie. You can’t tell me Celtic are not going to need another goalkeeper, so the guts of the squad could be ripped out.”
Celtic’s next outing in the Scottish Premiership comes against Motherwell on Saturday afternoon, with their opponents looking to make it three wins on the bounce in the league.