Klinsmann, who won the 1990 tournament with Germany as a player before leading Die Mannschaft as coach to third place at the 2006 World Cup, has called on one of his closest friends to scout his chances of taking over as Australia boss.
Newscorp reports the 53-year-old made an inquiry to Football Federation Australia about the role after Ange Postecoglou stood down last week, only days after leading Australia to its fourth consecutive World Cup.
However, Klinsmann's potential wage demands could be a major roadblock to his hopes of taking the reigns in Russia.
The former Bayern, Inter Milan and Tottenham striker would need to take a significant pay cut from the reported $3.3 million a year salary he earned in his most recent position as USA coach, with the FFA believed to have only a budget of $1.5 million per year for the role.
According to the Newscorp report, Klinsmann likened the Socceroos gig as a similar challenge to what he faced during his time in charge of the US national team.
Klinsmann called on his friend, who also works with him, to contact a former Socceroos player to get a better idea of the strength of the A-League, the Socceroos' depth of talent and their chances at the World Cup in Russia.
Klinsmann has coached 132 international matches during his career winning 75.
As well as leading Germany to third place at the 2006 World Cup, Klinsmann has also guided the US to the round-of-16 at the 2014 World Cup in Brazil.
He was sacked as US coach in November after a run of poor results which ultimately lead to the side missing World Cup qualification for the first time since 1986.