Former Socceroos striker Robbie Slater has called for Postecoglou to stick with the national team and turn down a reported $A3.8 million deal with Chinese Super League (CSL) outfit Shanghai Shenhua.
"No, you don't go there. You're national coach, you stay until it's done," Slater told Sky Sports Radio on Tuesday.
"We're talking about our country and a commitment and (if) you make all the statements you have, then you stay.
"If you are going to go, tell us. Be honest. That's the only thing I'm accusing him of - not giving the finality of whatever decision has been made."
Reports surfaced following the last World Cup qualification game against Syria that Postecoglou would quit after next month's playoff matches against Honduras.
Postecoglou has made no secret of his desires to coach a European club at the end of his Socceroos contract.
That was to be at the end of next June's World Cup - should the Socceroos qualiy for Russia - or next month if Australia fail to beat Honduras in next month's home-and-away series.
No one expected the 52-year-old to walk away from the prospect of leading Australia to a World Cup.
If the Chinese speculation proves accurate, Postecoglou would be moving to a league he's denigrated both publicly and privately.
Last year, he said the A-League was "ahead" of the Chinese Super League "in the overall intensity and tempo ... and general level of the game".
Shenhua may not be the most attractive option considering its tough history with coaches.
Former English Premier League manager Gus Poyet quit his position in September - becoming the 15th head coach to leave in the past 10 years.
Retired star A-League striker Joel Griffiths, who played at Shenhua in 2012, warned any possible stint for Postecoglou in the CSL could be short.
"(Chinese players) have a different mentality. You have to make them believe in your system to get the best out of them," Griffiths, who now works in the football department of former club Newcastle Jets, told AAP.
Griffiths backed Postecoglou to blaze a trail for more Australians coaching in China should he choose to make the move.
"Ange has been successful wherever he's gone. His record speaks for itself. He's the best coach in Australia by a country mile," he said.
"If he does it right, he'll be okay.
"But it can be a short time if he doesn't. I've seen how quickly the dressing shed can shift. You have to keep control of the Chinese boys, particularly the leadership.
"It's a challenge, but if he can get the right people around him, I think he'll be fine."