The 35-year-old central defender was roundly castigated for his performances in successive 6-0 friendly defeats to Brazil and France which triggered the departure of coach Holger Osieck last month.
The German's successor, Postecoglou, has been tasked with regenerating the squad and Neill was widely expected to lose not only the captaincy role he has held since 2006 but perhaps also his place in the 23-man squad Australia will take to Brazil.
While fellow veteran Mark Schwarzer retired on the eve of Postecoglou's first squad announcement, Neill was included in the party that has gathered in Sydney this week for next Tuesday's friendly against Costa Rica.
"Right now, there's 23 guys on trial all looking to stake their place in a World Cup squad," Neill told Australia's Channel Nine TV on Wednesday.
"I have a chance now this week to impress the new manager and hopefully my natural leadership qualities will come through and I'm one of the players that gets picked for that 23.
"I'm a very proud Australian, I still feel I have plenty to offer the team."
The former Blackburn, West Ham United and Everton defender has played 95 times for his country, including all of Australia's matches at the 2006 and 2010 World Cup finals.
Now playing his club football in Japan with Omiya Ardija, Neill has often been outspoken and responded for calls for a rejuvenation of the Socceroos squad by saying that it was up to the younger players to force their way in.
While he said he had no idea whether he would be retained as captain next week, Neill has no intention of relinquishing the role without a fight.
"Obviously I have the experience of being a leader and I'm always going to hold my hand up and offer myself for that honour," he added.
"But like always, I'll consider myself a role model and I know I have responsibilities to this country and I'll continue to do that as long as I get the opportunity."
(Reporting by Nick Mulvenney; editing by Peter Rutherford)
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