Moore, a defender with Rangers during his playing days, was an advisor to the Australia World Cup set-up under Postecoglou in 2014 and for the successful Asian Cup campaign a year later, and has always expected success from the coach, “a winner wherever he has been”.
Celtic fans had been expecting Eddie Howe as the next manager, instead the Australian emerged as a shock candidate on Friday and prompted much research, though Moore has first-hand knowledge.
“I’m not surprised that he’s a name that has come up because I’ve worked with him and believe he’s a very good coach, capable of reaching a good level, and it was just a matter of when – it looks like that time might be now,” he told The Scotsman. “It’s not Ange Postecoglou’s problem that people don't have a lot of information on him. It's certainly not through lack of achievement on his part – he has won trophies wherever he has been.
“But fair play to Celtic. They’re looking outside the box which is brave to do.
“He is the main coach from Australia who has broken through and done something a little different, success with the national team and then in Japan. He is a pioneer and a lot of coaches look up to him.”
His brand of football, recalled by midfielder Jackson Irvine in a recent podcast was ‘hectic’, but Moore believes the dominating, all-energy play would be a hit with supporters.
“He plays an entertaining brand of football which I think will appeal to Celtic supporters. His teams tend to have the ball a lot, and score a lot of goals so I think it’s quite entertaining.
"Look at the modern-day coaches, Bielsa, Klopp if you don’t have good energy to get about that field you’re not going to suit the way he wants to play. It’s full-on energy, dominating the ball, working really hard to suffocate teams even when they have the ball. Domestically the majority of games Celtic dominate possession, so it’s a good starting point.”
Winning though is what Celtic are also seeking. Substance as well as style following their first fallow season in a decade but with a winner internationally and on two continents, Moore believes they are looking in the right places.
"Ange always aimed to better himself. He will know the pressure of the Old Firm, especially on the back of a season without success. Winning is the only way that can be turned around. He understands that – remember he’s not a rookie.
"He would definitely improve Celtic. No doubt about that. He seems to get the absolute maximum from everyone, and that can’t be a bad thing.
"He’s big on creating a culture of belief and confidence among the people around him, who do things and do things well. Everyone is on their toes and everyone contributes, he doesn't carry passengers.
"The most important thing for Celtic is to get back to winning ways – and he is a winner – but it’s no secret who I used to play for, so maybe close second would do!”