Postecoglou previously declined to clarify his position when, the day after Australia beat Syria in the Asian playoffs, reports in local media said he was planning to resign whatever the result of November's clashes with Honduras.
The 52-year-old is contracted until the end of Australia's World Cup campaign, whether that comes next month or next year in Russia, and he has indicated he would be not be seeking a new deal.
On Monday, Postecoglou will appear in a biographical program on the ABC but a segment pre-released on social media indicated there would be no great revelations.
"It's a real kind of a facetious question because people just want me to fit into their stereotype and answer it in a way that makes themselves feel really good about themselves," he said when asked whether he was planning to step down.
"If people are really worried about my future, they should be worried about these two games, but they're not, they just want an answer to a question, and I'm not going to give them it.
"Everyone else wants me to behave a certain way and I'm just not like that, I've always done things my own way and I always will."
Postecoglou led Australia to their only major trophy in 2015 when they won the Asian Cup on home soil but has come under fire over his tactics as the World Cup qualifying campaign faltered.
The Greek-born former Brisbane Roar and Melbourne Victory boss has made no secret of the fact that he would one day like to test his coaching skills overseas.
Australia face Honduras in San Pedro Sula on November 10 with the return match in Sydney five days later. The winners on aggregate will secure the final spot at next year's finals in Russia.
Football Federation Australia CEO David Gallop said on Monday the governing body would not be caught on the hop if Postecoglou did decide to walk away in November.
"Football is fluid, people move. We'll adjust to that I'm sure," he told reporters in Sydney.
"The Socceroos don't play again until March, so we've got a relatively long stretch of inactivity. That will give us an opportunity to make a decision with Ange about the future."