Spurs have witnessed managerial turmoil this season after the successive departures of Antonio Conte and Cristian Stellini and their caretaker manager Ryan Mason is unlikely to be given the job beyond the summer.
The north London outfit were heavily linked with Feyenoord coach Arne Slot as their next manager.
But the Dutch coach revealed on Thursday that he wishes to stay in the Netherlands for the time being.
And Spurs are now turning their attention to Postecoglou, who has also been on the London outfit’s managerial shortlist.
Sutton feels that Tottenham will still be attractive to the Celtic manager as the north London side, even after an apparent disastrous campaign this term, remain a big club at the top end of the Premier League.
He also added that the London outfit have huge potential and feels Postecoglou will have the belief to succeed at Spurs.
“I know Spurs have their issues but this is not a club struggling at the foot of the division in danger of relegation”, Sutton said to the Daily Record.
“Even after an apparently disastrous campaign, they have still been in the running for the Champions League places.
“When you look at the stadium and the finances, there is huge potential.
“There’s been problems, of course. Jose Mourinho and Antonio Conte – two of the best managers in the world – couldn’t crack it at Spurs.
“But watching Postecoglou, he will have the self-confidence and belief he could be a success there.”
It remains to be seen whether Tottenham strike a deal for Postecoglou or continue their search to fill their managerial hot seat.