Postecoglou’s name has cropped up whenever a Premier League job becomes available in the last few months.
He is believed to be on Leeds United’s radar but it is highly unlikely that the Australian will leave Celtic for a fight to survive in the Premier League in the middle of the season.
Sutton does not believe Postecoglou will consider leaving Celtic unless a top Premier League job becomes available south of the border.
And he feels that could work in Celtic’s favour as the snobbery of the big Premier League clubs might stop them from wanting Postecoglou over a more fashionable name from Europe.
The former Bhoy wrote in his column for the Daily Record: “However, the more he succeeds, the more people are going to look at him.
“That’s only natural.
“One thing to consider which may work in Celtic’s favour when it comes to English interest is a snobbery that could well come into play.
“My own feeling is that, unless it were a really top job south of the border that became available, the Aussie would not be interested.
“And, when I think of how the very top clubs in England would go about potentially filling posts in the modern game, I harbour lingering doubts about them looking towards Glasgow.”
Postecoglou has already won a Scottish Premiership title and is in course to help Celtic retain the title this season.