The Yokohama F. Marinos boss is the frontrunner to succeed Neil Lennon at Celtic Park, having been on the club's radar since February, and after talks with Eddie Howe broke down last week the 55-year-old is now the favourite.
Ryan McGowan, who had spells in Scotland with Hearts and Dundee United, played under the Greek-born coach at international level and rates him as one of the best coaches he’s played under – but insisted Hoops fans won’t be getting a “yes man” if the former Melbourne Victory coach is appointed.
Speaking to BBC Scotland McGowan said: “Celtic aren't getting a nobody just because people haven't heard of him. If fans do some research on his style and approach, I'm pretty sure they'll be happy.
"He has had success everywhere he's been and he's definitely one of the best coaches that I've worked with. I'm pretty sure, if Celtic get him, that he'll do a very good job there."
Postecoglou led the Socceroos to the 2014 World Cup and 2015 Asian Cup success but stood down four months before the 2018 World Cup.
McGowan explained: “He's definitely not a ‘yes man’ – he left four months before the World Cup. He wasn't happy with some of the decisions taken above him so he walked away.
"I have no doubts he will be setting his demands in terms of what he wants from the job and, if Celtic don't match that, he won't take it on."
Postecoglou sets up his teams to play in a very specific style – so much so that his Brisbane Roar team was christened “Roarcelona”.
"He's very stubborn in terms of how he wants to play. All his teams play exactly the same way: a possession-based style, with emphasis on scoring as many goals as possible. He's not a coach that sits back on a 2-0 lead,” McGowan added.
In terms of his management style, Postecoglou is “clever… and a bit stand-offish”: “He’s the boss and what he says goes. It’s his way or the highway; there’s no in-between. Unless you buy into it, you’ll be out the door,” McGowan explained.
"But there aren’t many players who would say a bad word about him. He is very meticulous in everything that he does. His training sessions were down to the minute. He is different class with how he motivates.
"If he goes to Celtic, it will be interesting to see how he handles the scrutiny. There aren’t many clubs in the world with the same kind of pressure and that will be new to him.”
Postecoglou himself wouldn’t be drawn on the link with Celtic after leading the Marinos to a 2-1 J-League victory over Shimizu S-Pulse, insisting that his focus had been on the clash at the Nissan Stadium.
"I’ve understood there’s some speculation around the future, but I’ve stopped thinking about the what-ifs in the world a long time ago,” he said after the game.
"This is the job I’ve got, and I’ve always done that my whole career. I’m just focused on the job I have and making sure I do it well — or else other people will decide my future.”