RNA - Under Australian law, anyone intercepted trying to reach the country by boat is sent for processing to detention centres on Manus Island, off Papua New Guinea (PNG), or the Pacific island of Nauru.
They are never eligible to be resettled in Australia.
"Both Papua New Guinea and Australia are in agreement that the center is to be closed," Papua New Guinea Prime Minister Peter O'Neill said in a statement on Wednesday, following a meeting with Peter Dutton, Australia's immigration minister, Al Jazeera reported.
"A series of options are being advanced and implemented. It is important that this process is not rushed out but carried out in a careful manner."
There was no mention of a closing date.
Some asylum seekers have spent years in the camps, which have been criticized by the United Nations and human rights groups, with numerous reports of abuse and self-harm among detainees, including children.
Some in PNG are unhappy at the prospect of hundreds of asylum seekers being resettled into their country, and there have been reports of refugees being attacked by locals.
Australia says the policy is needed to stop asylum seekers dying at sea on the dangerous boat journey from Indonesia to Australia. Hundreds of people died attempting the trip in the years before the policy was put in place.
Following his meeting with the PNG leader, Dutton reiterated Australia's position that it would not accept any of the refugees held in Manus.
"It has been the long-standing position of this government to work with PNG to close Manus and support those people as they transition into PNG or return to their country of origin," Dutton said in a statement.
"Our position, confirmed again today with PNG, is that no one from Manus Island Regional Processing Centre will ever be settled in Australia."
The announcement came after a newspaper published leaked documents detailing more than 2,000 incidents of sexual abuse, assault and attempted self-harm, reported over two years at the Nauru detention center.
The harsh conditions and reports of systemic child abuse at the camps have drawn wide criticism at home and abroad.
"In April, there was a court ruling in Papua New Guinea saying that the prison camp was unconstitutional, and Papua New Guinea has made it clear that they have wanted that camp to close," Al Jazeera's Andrew Thomas, reporting from Sydney, said.
"But this is the first time that Australia has suggested that it's signed up to that as well."
Also on Wednesday, protesters in Sydney interrupted a speech by Australian Prime Minister Malcolm Turnbull, demanding the closure of offshore prison camps.
Numerous people in the audience shouted "Shame on you" and "Shut down Manus and Nauru", before they were escorted out of the event by security.