Nauru intends demanding more control over Australia's asylum-seekers than it had under the previous government's policy of processing them abroad.
The Australian newspaper reports Nauru's Foreign Minister Kieren Keke as saying the island had pretty much handed over to Australia the original detention centres, which operated between 2001 and 2007.
They were shut down by Australia's Kevin Rudd-led government in 2008, but Australia now again wants to process boatpeople in other countries.
An Australian team of defence and government personnel arrived on Nauru last Friday, and terms could be worked out to allow asylum-seekers to be housed there within weeks, possibly in tent accommodation.
Dr Keke says this time around Nauru is happy to host the centre, but will want it to be much more under Nauruan control.
He says this time it would not be a 'fee-for-hosting' deal.