The 49-year-old was sacked by the Hammers in early November, after a 4-1 loss to Liverpool at the London Stadium saw his future become untenable in the eyes of the east London outfit's owners.
He has since been linked with numerous roles, including the USA men's national team, while a return to the Premier League has also been on the cards with Bilic at short odds to join Swansea City and most recently, Stoke City.
However, Bilic could be now tempted to return to international management after a six-year stint in charge of Croatia between 2006 and 2012, with the World Cup in Russia just months away.
The report claims David Gallop, chief executive of the Australia Football Federation, has had multiple conversations with Bilic's representatives over a move down under while scouting European candidates.
The FFA claim they will not appoint anyone to the role until mid-February, with RB Leipzig's sporting director Ralf Rangnick and former Torino boss Gianni Di Biasi also being considered.
The Socceroos, who boast players such as Premier League stars including Huddersfield's Aaron Mooy and Brighton's Mat Ryan, are on the lookout for a new manager after Ante Postecoglou resigned in November.
Australia have a strong chance of making it out of Group C and into the knockout rounds, after being drawn against France, Denmark and Peru. With France likely to win the group, Australia would need to get a result against Denmark.
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