The former Socceroos boss is hotly tipped to be named Celtic manager - possibly in the next few days - and, if a deal is sealed, he will face an instant test of his credentials.
The Hoops, who are hellbent on wresting domestic supremacy from crosstown rivals Rangers, have been served a nightmare draw in their bid to reach the UEFA Champions League because, as league runners-up, they cannot access the competition via the champions' route.
What lies ahead is a qualifier against Turkey's Galatasaray, Denmark's Midtjylland or Austria's Rapid Vienna, starting on July 21-22, which is only seven weeks away.
Should they overcome that two-legged hurdle, the Hoops will then face Belgian runners-up Genk, Dutch giants PSV, Russia's Spartak Moscow or Sparta Prague from the Czech Republic, provided the prospective opponents get through their own ties.
If Celtic win that second qualifier they will be up against Shakhtar of the Ukraine, Monaco or Portugal's Benfica for a spot in the lucrative 32-team tournament.
The former Socceroos boss would not be overawed by this stiff challenge. If anything, it would motivate him even more.
Setting aside the Champions League issue, it remains to be seen if Postecoglou would get to enjoy a stint in 'Paradise' - which is how Celtic Park is affectionately known by the club's supporters.
Many suspect that his inexperience of European football - never mind the British game - would be his undoing. Managing Greek third division side Panachaiki for a few months is hardly a CV to turn heads.
Others fear he might be unprepared for the intense scrutiny he would inevitably face on a daily basis in one of Europe's most passionate football cities, particularly if results do not meet expectations in the first few weeks of the season.
These concerns no doubt are more than justified - European football at a certain level is not for the faint-hearted - yet many are missing the point of this startling development.
The fact that our most prominent coach has been approached to manage such a famous club is testament not only to Postecoglou himself but also to the game in Australia which nowadays enjoys a decent reputation abroad thanks largely to the feats of such stars as Mark Viduka and Harry Kewell.
Celtic's belief in Postecoglou becomes all the more remarkable when you consider that Australian coaches are largely unknown in Europe because, unlike some of their playing counterparts, they have absolutely no reputation to speak of.
This will not bother Postecoglou one bit, of course, because he is a good coach, he knows he's good and every player he has managed knows it too. He certainly has the runs on the board.
After leading South Melbourne to two national titles in the 1990s, he took over the national youth team but his stint with the Joeys from 2000 to 2007 was largely unsuccessful and he was dismissed.
It was the low point of Postecoglou's career. He has admitted that at that stage he considered himself "unemployable" ... but in 2009 he got a lucky break.
After a chance meeting with then A-League head Archie Fraser, one thing led to another and before he knew it he was named as head coach of Brisbane Roar.
The appointment would be the turning point of his career because in a short time he transformed an under-achieving side into serious A-League contenders, winning two straight titles with a style of high-octane, possession-based, attacking football that had never been seen in Australia.
His reputation as an avant-garde coach rose with every match and it was always going to be a matter of time before he got the appointment he yearned for since he took on coaching: the Socceroos job.
In 2013, Postecoglou - after a brief stint with his hometown club Melbourne Victory - took over the national team when Holger Osieck was sacked.
The Socceroos had already qualified for the 2014 World Cup under the pragmatic German when Postecoglou took over and he spared no time in trying to build a culture of no fear, which essentially meant having a go even against the world's strongest teams.
His players failed to win any points in the group matches against Chile, Netherlands and Spain in Brazil but their bravery and spirit of adventure left a favourable impression and showed that they were buying into Postecoglou's positive preachings.
Six months later, the Australians won the first major honour in the country's history by snaring the AFC Asian Cup after a thrilling 2-1 win over old rivals Korea Republic in Sydney.
It was a deserved triumph that vindicated Postecoglou's refreshing approach. Always the deep thinker, he said after the final he hoped the victory would obliterate the inferiority complex that had adversely affected Australia's progress for decades.
Postecoglou was hailed as a messiah but the honeymoon did not last long.
Dark clouds started gathering over the Socceroos set-up when results and performances in the qualifying rounds of the 2018 World Cup caused consternation.
Postecoglou's tinkering with the formation drew criticism from the media and, for the first time, the coach who always came across as one who was supremely confident in his judgment and ability began to show signs of frustration.
Matters came to a head when it was sensationally revealed he would quit his post at the end of the Socceroos' qualifying campaign, regardless of the outcome.
The news came as a shock and what made matters worse was Postecoglou's refusal to fully explain his decision.
The Socceroos scrambled into the finals in Russia via two playoffs and were led by Dutch ring-in Bert van Marwijk.
Postecoglou in the meantime was working on his newest project - that of turning Yokohama F. Marinos into J.League champions.
He did this in his second season and the club were able to savour their first championship in 15 years.
Yokohama are part of the powerful City Football Group and his success in Japan would have alerted the Abu Dhabi-based organisation and the football world of his growing stature.
Celtic know exactly what they are bargaining for, no doubt about that.
