The German legend, who was sacked in 2016 after a poor start to the Americans’ World Cup qualifying campaign, commissioned one of his closest friends to scout out the Socceroos job, according to The Adelaide Advertiser and other media late Sunday.
The 53-year-old made the inquiry after Postecoglou walked away to pursue overseas opportunities despite leading Australia to the international showpiece in Russia next year.
He is reportedly the frontrunner to take charge of J-League club Yokohama F-Marinos next season.
According to The Advertiser, Klinsmann’s friend quizzed a former Australian international about the quality of the domestic A-League, the strength of the national team and the likelihood of Australia being competitive in Russia.
He is said to be interested because “Australia has a very similar sports landscape to the US”, but could be put off by the salary on offer.
Broadcaster SBS said Football Federation Australia was believed to only have a budget of Aus$1.5 million (US$1.14 million) per year for the role, which would be half what the German was paid by the United States.
Australia have been drawn in a tough Group C at the World Cup, along with higher-ranked teams France, Denmark and Peru.
They play France in Kazan (June 16), Denmark in Samara (June 21), and Peru in Sochi (June 26).