Postecoglou, who took up the role in 2013, will walk after next month's intercontinental play-off against the fourth-placed CONCACAF nation regardless of the result, News Corp reports.
He reportedly would have quit last month even if the Socceroos had qualified automatically for Russia 2018.
But after finishing third in the group behind Saudi Arabia and Japan, Postecoglou felt compelled to stay on and guide the Socceroos through their playoffs.
The Socceroos cleared the first hurdle with a gripping 2-1 win over Syria on Tuesday night, winning the tie 3-2 on aggregate after a 1-1 draw last week.
Football Federation Australia were scrambling to ascertain all the facts after the bombshell broke on Wednesday, with chief executive David Gallop understood to have been unaware of Postecoglou's intentions.
A subsequent statement suggested FFA was blindsided by the news but Gallop said he had spoken to Postecoglou.
"Should we qualify, there is a period of some months until the World Cup and we agreed that we will need to lock in our set-up as soon as possible to maximise our preparation time," Gallop said in the release.
Postecoglou himself said he was "aware of reports".
"I am aware of reports today suggesting that I will step down as head coach of the Socceroos next month," Postecoglou said.
"My sole focus is on preparing the team for our final two qualifying matches.
"I will not let anything compromise the team's journey on getting to a fourth consecutive FIFA World Cup."
The 52-year-old's shock decision is reportedly prompted by the scathing criticism he has received over recent months.
Sources close to Postecoglou have confirmed that the final whistle on his Socceroos tenure will blow next month.
“He is definitely moving on after November,’’ a source close to Postecoglou said.
Postecoglou, who's contract ends at the conclusion of this World Cup cycle, offered no hints he was bringing his exit forward after Tuesday night's 2-1 win over Syria.
He has received scathing criticism over recent months over his unapologetically expansive philosophy and mid-qualification formation change.
The Asian Cup-winning mentor's departure would leave an enticing World Cup coaching spot free if Australia make it past their next opponent from CONCACAF - Honduras - in November.
Postecoglou was in customarily combative form following Tuesday's 2-1 Syria win, sealed by two Tim Cahill headers.
"It just astounds me that people keep thinking this is supposed to be easy," he said.
"You saw what it meant to the opposition tonight. It's going to mean the same for the other opposition.
"I just don't get it when people think it's supposed to be some ... show me the evidence that we've cruised through to a World Cup.
"Even the first year in Asia we got through strong under Pim Verbeek, fantastic performance but we weren't smashing teams. Last time we got through in the last game.
"There is no evidence to say that anyone in this confederation is easy ... if people think we go into games thinking we're going to smash the opposition here because we're that far superior, they haven't been watching."