Football Federation Australia said on Tuesday it had formed a nine-person panel and engaged a consulting firm to assess candidates to take Australia to the World Cup in Russia and beyond.
Postecoglou announced his resignation last week after four years in the role, having recently secured Australia's qualification to a fourth successive World Cup.
FFA chief executive David Gallop said last week that the governing body's preference was for another Australian coach but on Tuesday said they were keeping their options open.
"As things stand, no-one is ruled in or out," he said in a statement.
"We are open minded about whether the coach is Australian or someone from overseas but they must live in Australia, embrace the progress on and off the field that has been achieved with national teams over the past four years... and be prepared to be an ambassador for our sport here and abroad.
"FFA's starting point is to appoint a coach for the long term but we will be advised on this and other matters by our expert panel."
A number of high-profile international coaches have been linked with the role but Eriksson became the first to declare his interest publicly, according to a report in Melbourne's Herald-Sun newspaper on Tuesday.
"Yes of course I'm interested. It's a big job, a big football country, you're playing in the World Cup — again. You more or less always play in the World Cup," the paper quoted the Swede as saying.
Slavoljub Muslin, who was axed after successfully guiding Serbia through Russia qualifying, was also reported to be a candidate last week, with Graham Arnold and Tony Popovic seen as the strongest local contenders.
(Reporting by Ian Ransom; Editing by Sudipto Ganguly)
