Sutton said that while he rated Rogic "extremely highly", the 26-year-old's position was in "serious danger" of being taken by Ryan Christie.
"The Australian is a magician with the ball at his feet and it was no secret I was delighted when Celtic managed to get him on a new contract at the tail end of last season," Sutton wrote in the Daily Record.
"However, if the truth is told there are warning signs flashing now for Rogic.
"And his mantle is in serious danger of being taken by Ryan Christie who is developing into the No.10 the club always hoped he’d be when he was signed by Ronny Deila."
Rogic suffered at Celtic last season due to injury and AFC Asian Cup duty, only starting 26 matches for the club last season.
24-year-old Christie started 30 matches for Celtic last season, managing to score 11 goals and create 9 assists compared to Rogic's five goals and six assists.
Sutton pointed to the Rogic's injury history as part of the reason he might be spending more time on the bench.
"(Rogic is) developing a knack for missing games and if Christie can keep himself fit and firing it might just be the case the Aussie has to stand aside.
"What Christie lacks in terms of Rogic’s traits he more than makes up for with his speed and his workrate.
"The 24-year-old is full of invention but, crucially, he’s also full of energy.
"Neil Lennon likes his teams to play with a tempo and it is most certainly increased when the former Inverness Caley man is on the pitch.
"Not only does it make them more urgent when they are in possession it gives Celtic a chance to win the ball back much higher up the pitch and get at teams faster.
The former Central Coast Mariners midfielder was a favourite of former Celtic boss Brendan Rodgers who joined Premier League side Leicester City in January.
However under new coach Neil Lennon, Christie has been seeing more minutes. Sutton suggested that the trend should continue this season.
"Rogic remains a fantastic player and I would far rather he stayed.
"He has had some injury issues and it’s not fair to judge him on the past few months when he has been fighting to get back to peak form and fitness.
"But the man (Christie) in possession of the jersey is doing the business.
"If anything, Christie is stamping down a marker that HE is the one Lennon sees as his Perfect 10."
Celtic next play on July 31 in the UEFA Champions League second round qualifiers against Nomme Kalju.
