Van Gaal was in charge of the Netherlands side who finished third at the last World Cup in 2014, which saw him record an impressive 5-1 victory over Spain and also a memorable 3-2 victory over Australia.
On top of this, he is best known for winning the UEFA Champions League in 1995 with a very young Ajax side, with whom he also won three straight Eredivisie titles, and for most recently leading Manchester United from 2014 to 2016.
The opinionated Dutchman also won league titles with Barcelona, Bayern Munich and AZ. It was at AZ where he worked with Australians Brett Holman, James Holland and the Geelong born goalkeeper Joey Didulica.
According to a News Limited report, FFA has made contact with van Gaal who has expressed interest in the job.
Van Gaal, 66, has been out of work - although this is understood to be by choice - since departing Manchester United after winning the FA Cup in 2016.
In a recent interview with The Daily Mirror, van Gaal said he wasn't interested in coaching at club level anymore, with one exception.
“I would make one exception — if a big English club comes for me, than I would do it. Because then I can get the chance to get one over on Manchester United,’’ van Gaal said.
He did not make any comments regarding taking over a national team.
While his Ajax side of the mid-1990s was synonymous with entertaining, attacking football, his latest work with Manchester United was widely criticised for being 'boring'.
The 2010 Champions League runner-up with Bayern Munich, is the latest big name international coach to be linked with the job, after Marcelo Bielsa, Luiz Felipe Scolari and Jurgen Klinsmann have all been rumoured to be interested in the job.
FFA have previously announced that the next Socceroos coach will be chosen by a nine-person panel, including former international stars Marco Bresciano, Mark Schwarzer and Stan Lazaridis, with an announcement expected in mid-Ferbraury.
Australia will face France, Denmark and Peru at the 2018 World Cup in Russia that kicks off in June.