Papua New Guinea's Supreme Court ruled this week that the facility was unconstitutional.
Australia sends asylum seekers there under its offshore processing policy.
Papua New Guinea's high commissioner to Australia Charles Lepani said the detainees were Australia's responsibility.
Australia has remained opposed to taking any of them.
Immigration Minister Peter Dutton said on Thursday there was room for them at another detention centre on Nauru.
"There's capacity [on Nauru] but we're talking with the PNG government about what options are available in PNG and we'll continue those discussions with them," Mr Dutton said on Sky News.
This comes after an Iranian asylum seeker held at the Australian-funded detention centre on Nauru set himself on fire on Wednesday.
His actions were a "political protest" according to the Nauruan government.
Mr Dutton said the 23-year old man was in a serious condition and was evacuated to Australia for treatment.
Nauru is a small Pacific Island nation about 3,000 km (1,800 miles) north-east of Australia.
It was previously administered by Australia but gained independence in 1968.
Manus Island: a controversial 'solution'
The camp first opened in 2001 under Australian Prime Minister John Howard.
It was formally closed in 2008, but reopened in 2012 when a spike in asylum seeker arrivals became a major political issue for the Labor government.
In 2013 Australia agreed to give Papua New Guinea A$400m ($309m; £212m) in aid in exchange for housing a camp and to resettle genuine refugees.
Deadly riots broke out in February 2014 when local residents entered the facility. In January 2015 some detainees barricaded themselves inside their compound and went on hunger strike.
Private security contractor Broadspectrum, formerly Transfield Services, currently runs the camp.
Australia's government says its refugee policy has led to a sharp drop in the number of migrant boats.
UN agencies and rights groups have criticised conditions at the camp and say Australia is shirking its responsibilities towards refugees and migrants.
This post was written by: Raymond Jack
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