The Greek-born boss of Japanese side Yokohama F. Marinos is the clear favourite to take the reins at Celtic Park and Milligan, who played under Postecoglou at Melbourne Victory and for the Socceroos, believes his former coach can be a big hit in Scotland.
“I don’t think it’ll take long for the Celtic fans to understand what he’ll bring, and what the team will be about,” Milligan told the Sydney Morning Herald.
“I haven’t worked under him for a long time but I’ve got a fair idea of the way he works.
"It doesn’t look like that’s wavered over the last few years, the way his Yokohama team play. Giving him the quality of player that Celtic provide is only going to enhance his reputation.”
Postecoglou has only managed club teams in Australia and Japan but Milligan, who experienced Scottish football during a spell with Hibs in the 2018/19 season, is adamant that the 55-year-old’s approach to the game will fit in well with Scottish football.
“They’re very, very passionate [in Scotland]. I know Tommy Rogic still has problems going for a coffee and stuff like that,” he added.
“They’re the places you want to be as a footballer, that environment, that fanatic attitude towards the game.
"Celtic’s fans and the history of that club is not rivalled by too many. You see the passion and what it means to them. If you’re able to be a part of it and better it, it’s a wonderful place to be.”
Milligan is following his own path into football management, having this week announced his retirement from playing and intention to serve as assistant manager to Ante Milicic at his current club Macarthur FC.
He believes Postecoglou taking the Celtic job could be invaluable to changing the narrative about football in Australia.
“If Ange goes there he’ll bring a brand of football that the UK will enjoy and that will open doors down the track, maybe start to get rid of the stigma of what we are and what we’re about.
"We’ve adapted and changed as a footballing nation.”