Football Federation Australia chief executive David Gallop has left the door open for Guus Hiddink and Gerard Houllier to coach the team at the 2014 World Cup.
The Socceroos' 6-0 loss to France on Friday resulted in the dismissal of Holger Osieck, who oversaw a disastrous streak of defeats to Japan, China and Brazil in recent months.
While leaving the door ajar for Hiddink - who led the Asian giants in the 2006 World Cup - and Houllier, Gallop said nationality did not matter so much as the new boss' ability to restore success to the team.
"It certainly makes sense to have an Australian coach but whether that makes sense right now, is something we need to look at seriously over the next few weeks," he told reporters in Paris.
"We're always exploring options and at the moment that's all we're doing. It's not appropriate to go into who has been contacted and who hasn't but obviously some feelers have been put out.
"This is about the need to rejuvenate, regenerate our team. We've got a lot to look forward to in the next months and years.
"Obviously Brazil is important as is the Asian Cup 2015 and ultimately we want to be at the next World Cup as well. This is a decision taken in the long-term interests of the team.
"We'll hopefully have some definitive answers on that over the next few weeks."
Hiddink has enjoyed notable stints leading Asian outfits at the World Cup, taking South Korea to an unlikely fourth-place finish in 2002 before his Australia side only fell 1-0 to eventual winners Italy in 2006.
Houllier, meanwhile, took charge of France at senior and youth levels between 1992 to 1997, before moving to boss a succession of club sides including Liverpool, Lyon and Aston Villa.
Both candidates are presently unemployed.