There is understandable talk of the former Australia boss staying on to lead the team to the AFC Champions League title.
Completing the treble: the Asian Cup, a major domestic league trophy and the continental club championship would put Postecoglou in the middle of the podium when it comes to the best Asian coach ever. It would be an incredible thing to do.
But if his ultimate goal is to coach at the highest level of club football - which is the big leagues of Europe - then he should leave before the sweaty fingerprints on the trophy have had time to dry.
Winning the 2020 Asian Champions League, a far from foregone conclusion, would go down very well indeed in Australia and elsewhere in the AFC but would not substantially increase his reputation elsewhere.
There is no clamour among the big clubs of Europe to sign Razvan Lucescu, the man who just led Al Hilal to the title, just as there was no interest in Choi Kang-hee, the South Korean who delivered two continental titles for Jeonbuk Motors.
The example of Dragan Stojkovic is a striking one. Nine years ago I interviewed the Serbian legend at the Nagoya Grampus clubhouse. It was just before he led the club to their first ever title.
His stock was high and there were already some big teams sniffing around. What he wanted, however, was Arsenal, and for a while, it seemed as if the feeling was mutual.
‘Pixy’ had played under Arsene Wenger in Japan and was the proverbial lieutenant on the pitch, absorbed everything he could and kept in touch after the Frenchmen left.
A regular visitor to London to see his former mentor, Stojkovic was very close to the top of the list of possible replacements for Arsenal at the time. It is easy to see why: this former disciple had gone one further than his mentor and actually won the title in Japan.
As it turned out, the Arsenal job was not to be available for a few more years but Stojkovic may regret hanging around at Nagoya.
The team finished second the following season and reached the last eight of the Champions League but then proceeded to slide into mid table with a seventh-placed finish in 2012 and then 11th the year after.
Stojkovic left after that but he was rarely mentioned as a future Arsenal boss. In 2015, he moved to China and has been in charge of Guangzhou R&F, last seen finishing 12th in the Chinese Super League.
He was following in the footsteps of past foreign winners. Guido Buchwald led Urawa Red Diamonds to a first title in 2006 but was sacked by struggling Bundesliga club Alemannia Aachen after just 14 games of the following season.
Oswaldo Oliveira won three J.League titles on the trot with Kashima Antlers but ended up back where he started in Brazil. Compatriot Nelsinho Baptista won in 2011 with Kashiwa Reysol and, after some detours, is back at the club.
Former Brazil international Toninho Cerezo won the J.League twice with Kashima Antlers but that was the highlight of his coaching career.
Not that many coaches have gone on from the J.League to have glittering international careers. Those that have managed to do so, have tended to not spend too long in the Land of the Rising Sun.
Arsene Wenger was there for just 18 months. He was there long enough to gain from the experience and make an impact before heading to Europe.
Carlos Queiroz was Wenger’s permanent successor at Nagoya. It was a change of philosophy for the club but like the Frenchman, the future Real Madrid boss did not hang around, spending a year there before saying ‘Sayonara’.
Luiz Felipe Scolari did not even manage half a season at Jubilo Iwata in 1997 before heading back to Brazil where he would end up in charge of the national team and winning the 2002 FIFA World Cup.
As a coach Ange Postecoglou is nothing if not forward-thinking but, if he is thinking about his future then, he could do worse than look back at the history of some of his foreign predecessors in the J.League.
