The All Blacks and the Wallabies were due to meet at Optus Stadium on August 28, but New Zealand Rugby (NZR) opted against travelling due to concerns over coronavirus.
Rugby Australia (RA) announced it was "incredibly disappointed" at the move, while Wallabies head coach Dave Rennie stated in no uncertain terms he was "bloody angry" over the decision.
Playing the Test in the United Kingdom or South Africa had been suggested as an alternative, but RA chief executive Andy Marinos hopes the trans-Tasman rivals can still do battle in Perth next month.
"We're working hard now with the West Australian government and the stadium to see if we can't move that to September 4," Marinos told Channel Nine on Sunday.
"We remain optimistic and confident we can get the game away eventually in Perth."
NZR chief executive Mark Robinson denied claims that RA had not been told that the All Blacks would not fulfil the fixture before it was announced.
He said: "We had calls right through from Wednesday, Thursday, we put something in writing on Thursday and then we spoke to them before anything was released.
"Certainly I know that senior All Blacks and Wallabies were discussing the situation and our players were making them aware of the reality of our situation."
NZR also announced the All Blacks' two home Rugby Championship Tests against South Africa – scheduled for September 25 and October 2 – will not be played in New Zealand following government advice that the Springboks would not be able to enter the country due to COVID-19 travel restrictions.