The Nauru Government says it believes the Australian run detention camp on the island will be formally closed by the end of next month.
The Nauru Government is concerned at the economic impact of the closure and formal discussions with two Australian officials are underway on the island this week.
Nauru Foreign Minister, Dr Kieren Keke, says he has also invited his Australian counterpart to visit to see first hand the problems faced by the island.
Meantime he says the last asylum seekers, a group of 21 Sri Lankans, is expected to be flown to Australia within days.
"There's a few remaining and I expect that probably within the week there will be no more asylum seekers left on Nauru. It is our understanding that the camp will be formally closed by the end of March if not earlier."
The centre reportedly contributes about 20 per cent to the island nation's $25 million US dollars GDP and employs about 100 locals.
Meanwhile, Australia's other offshore processing centre at Manus Island has held no asylum seekers since 2004 and is expected to close by June.
A spokesman for the Parliamentary Secretary for Pacific Island Affairs, Duncan Kerr, said future unauthorised arrivals will be processed within Australia.
He said they will shortly be initiating discussions with the PNG Government on the future of the Manus facility.