Lawyer Ben Lomai, acting for hundreds of detainees at the Australian-run facility, will ask the judges to order Manus’ closure within 48 hours, declare PNG is unable to resettle those held there and that all refugees and asylum seekers be returned to Australia.
Mr Lomai will also seek a further hearing to consider compensation payments for human rights breaches in the four years since the centre has been open.
Last week the Australian and PNG governments reaffirmed that they are seeking to shut Manus down but without clarifying the detainees fate.
Australian immigration minister Peter Dutton said that none of the Manus detainees would be resettled in Australia and offered no time frame for the closure.
Last week Fairfax media reported Manus has cost taxpayers $2b since it was reopened four years ago, with an average cost of $1m for each of the 2,000 people detained there.
Citing federal parliamentary library analysts as the source, Fairfax added there were hundreds of millions of dollars more in ancillary costs.
The Supreme Court is expected to set a full hearing date for next week.
