Tottenham finished eighth this season in the Premier League and failed to earn a spot in European competitions next season.
Spurs have been in search of a manager since Antonio Conte departed the club in March and this week they appointed former Celtic boss Postecoglou on a four-year deal.
Postecoglou comes to Tottenham on the back of a domestic treble with Celtic and Petrov is of the view that the Australian tactician’s ambition will be very high after joining the north London outfit.
The former Celtic star is confident that Postecoglou will want to put Tottenham back in the Champions League in his first season because the former Celtic boss would like to challenge himself in the Champions League.
He further added that if the new Spurs boss is given proper time, he might well win Tottenham the Premier League title in the future.
When asked what can be expected from Postecoglou in his first season with Spurs, Petrov told Sky Sports Scotland: “His ambition will be high.
“He will definitely try to put Tottenham Hotspur into the Champions League spots.
“He would like to challenge himself in the Champions League, because that is where he wants to be.
“Will they be looking to win the league? I do not think they have the squad or they have the capability of doing that yet.
“But if they trust Ange Postecoglou to build success there, he will manage to do that because he has proven that in the last couple of years in every club he has walked through.”
It remains to be seen whether Postecoglou will be able to make Tottenham competitive next season and put them back in the Champions League.