Advocaat has decided to stay with Russian club Zenit St Petersburg, Sydney's Daily Telegraph reported.
The top coaching position has been vacant since fellow Dutchman Guus Hiddink, who took both Holland and South Korea to World Cup semi-finals, left to coach Russia.
Graham Arnold, assistant to Hiddink, has filled in since Hiddink shifted focus to Russia at the end of the last World Cup.
Advocaat, 59, is also a former coach of the Dutch national side, and, like Hiddink, coached South Korea.
The former PSV Eindhoven and Glasgow Rangers coach was believed to have signed a contract in August with the FFA.
Arnold was criticised after taking the Socceroos to a disappointing quarter-final finish at the Asian Cup and is unlikely to be considered as anything other than a stop-gap coach.
FFA chief executive Ben Buckley told the paper he had contacted Advocaat's lawyers and Zenit club officials over the shock decision.
Zenit claimed the Russian premiership title this week and is believed to have offered Advocaat an enhanced contract to stay on.