German Holger Osieck was summarily dismissed as coach last weekend after Australia were hammered by France in Paris, the second time in a month they had lost 6-0 after a similar defeat to Brazil in Brasilia.
Although FFA chief executive David Gallop said feelers had been put out to Dutchman Guus Hiddink, who led the Socceroos to the last 16 at the 2006 World Cup, his boss Frank Lowy said on Tuesday that the next coach would be Australian.
"I've had no formal contact, as far as I'm aware the club may have had some contact from FFA," Postecoglou, 48, told reporters in Melbourne.
"If it comes my way and I'm considered for the position, it would be a great honour.
"I don't think it's a position you should really lobby for, if the powers that be find it in their wisdom to have a look at me and offer it to me it would be a great honour."
While Postecoglou was born in Athens, he moved to Australia as a young child and has developed a reputation for rebuilding teams, most notably in three years at the Brisbane Roar, where his revamped side won back-to-back A-League titles in 2011 and 2012.
That reputation would be particularly attractive to the FFA, who said Osieck's failure to bring a new generation of players through into the national team was a contributing factor to his dismissal.
Other Australian candidates being considered for the post, according to Lowy, were former Australia coach Graham Arnold and Tony Popovic, who led Western Sydney Wanderers to the A-League championship final in their first season last year.
Lowy also said that with next June's World Cup fast approaching and Australia's hosting of the 2015 Asian Cup just over a year away, he wanted the new coach in place within a couple of weeks.