News Corp reported on Monday the 69-year-old Swede is keen on taking Australia to the World Cup, which would be his fourth as a coach.
"Yes of course I'm interested," he is quoted as saying.
Australia are without a national team coach after Ange Postecoglou's departure last month.
The Greece-born Melburnian coached the Socceroos at the 2014 FIFA World Cup and became the first Australian to oversee a successful qualification effort for the tournament.
The chance to take a country to the World Cup has attracted significant interest from coaches across the world, but Eriksson is the first big name to publicly express his desire.
Jurgen Klinsmann, Marcelo Bielsa and Gianni De Biasi have been linked to the role, as have A-League bosses Graham Arnold, Kevin Muscat and Josep Gombau.
Australia were drawn with France, Denmark and Peru in next June's tournament, with Eriksson adamant the Socceroos can reach the knockout round.
"It will be a fight for second place between Australia, Peru and Denmark. I think the chances for Australia are good," he said.
"The whole world would say France is favourite to win that group, but second I think is very tight ... why not Australia?"
Sven Goran Erikson's managerial record