PNG's government announced two weeks ago that the controversial detention centre will close after the country's Supreme Court ruled that it was unconstitutional.
Each country has argued that the other is responsible for those detained there.
Neither Australia nor PNG have followed the court decision, with both sides poised to ignore the Supreme Court ruling for months.
The minister, Peter Dutton, says talks between the two countries about what do have been constructive, but says a resolution will likely take a couple of months.
Such a timetable will drag Australia's controversial immigration policy to the fore of the country's election campaign, with an election scheduled to take place on the second of July.
Australia's hardline policy of detaining anyone who tries to reach the country by boat on Manus Island or on Nauru has bipartisan support from both main parties.