However, the ex-Hoops striker admits that the Australian would be likely to depart the Parkhead club if one of the English Premier League's bigger fish come calling.
Postecoglou is drawing plenty admirers for his success at Celtic thus far, rebuilding the side from the failed 10-in-a-row bid under Neil Lennon to win back the title in his first season in charge, as well as the League Cup.
His side are currently on a 35-game unbeaten run domestically and already have a five-point advantage at the top of this season's Scottish Premiership following an impressive 4-0 dismantling of Rangers last weekend.
Celtic also drew widespread praise for the manner of their performance against Real Madrid in the midweek Champions League group stage opener, with 60,000 home fans singing the manager's name at full-time despite the 3-0 defeat.
Sutton accepts that the progress made at Parkhead under Postecoglou will attract interest but he believes the 57-year-old will not consider leaving the club unless a top-six EPL side come calling.
Writing in his Daily Record column, Sutton stated: "You are surely not going to go from that to leaving in the blink of an eye, especially not to, with the greatest of respect, Brighton and Hove Albion. Postecoglou backs himself and so he should. His CV is stellar. He has taken his country to World Cup Finals, he has won trophies wherever he has been.
"If you back yourself, you are going to be selective and not jump at the first opportunity that comes your way. The Premier League is regarded by many as the best league in the world.
"But Celtic are far bigger than the majority of teams who operate within England’s top flight and that is a fact. Like I’ve said, no disrespect to Brighton, but Celtic are miles ahead of them. I can’t see a coach of Postecoglou’s quality stepping down the ladder to go to England’s South Coast.
"If he keeps doing what he’s doing at Celtic and progressing the club the way he is, he will go one day, I’m sure. Too many people south of the border in high positions are taking notice of him.
"When the day comes for Postecoglou to leave and if it is to England, it’ll be to one of the bigger clubs, a top-six club. If it’s not there, I don’t think he’ll be going anywhere."