The Manus Island detention centre is due to close by the end of October.
Some in the offshore detention centres are due to be resettled in the United States under an agreement with the Obama administration which the Trump administration is honouring.
But there are concerns some Tamils could be excluded from the United States because of their links to the rebel Tamil Tigers.
The Australian government has to find ways of getting people out of the Manus Island detention centre because the Papua New Guinea High Court has ordered its closure.
That closure is due to happen by the end of October.
But there is speculation the United States may refuse to accept Tamil asylum seekers due to any links with the Tamil Tigers.
Some countries classify the Tamil Tigers as a terrorist group, and the US Patriot Act excludes people who have provided so-called "material support" to terrorist groups.
Amid those reports, former prime minister Kevin Rudd has re-entered the political fray.
His government announced four years ago asylum seekers arriving by boat would never be resettled in Australia.
Mr Rudd now says that arrangement with Papua New Guinea was for one year only, telling the ABC that successor Tony Abbott botched the implementation of the deal.
"Implementation of the agreement fell down appallingly under Abbott, who adopted an utterly punitive approach to asylum seekers, and then, subsequent to that, Turnbull has sought to continue the political advantage by keeping people in appalling conditions for a long period of time. This was entirely contrary to the provisions of the early agreement of July 2013, which stipulated UN norms as far as housing, accommodation, proper treatment. These have not been provided, and, therefore, the circumstances would have changed, which would then require them to be located elsewhere, including, if necessary, Australia."
But Immigration Minister Peter Dutton has told Sky News Mr Rudd created the problem by undoing Howard Government policies.
The Coalition has long argued those decisions by Labor made Australia an attractive destination for people smugglers and their desperate clients.
"Kevin Rudd had a situation of his own making. He undid John Howard's policies. And, through his own actions, Kevin Rudd and many of the people who were in his cabinet who consented to this deal, who now sit on the frontbench of Bill Shorten's ... of his ministry, those people made the decision to put people on Manus Island and to keep them there. And the thought that they were going to be there for 12 months is a complete and utter nonsense. It's a fabrication, it's misleading, it's deceptive."
Treasurer Scott Morrison was immigration minister for the first 14 months of the Coalition Government after Mr Rudd's government was defeated at the 2013 election.
He says Mr Rudd's claims show Labor was insincere on the issue of border protection.
"We always said at the time that the Labor Party, when it came to protecting the borders and the integrity of our immigration system, that their heart was never in it, it was all just a political stunt. And Kevin Rudd has proved once again that, when it came to border protection, his government and the complicit partners in that government, which include Chris Bowen, who was the immigration minister at the time, when it came to border protection, were complete and utter phonies."
Labor has adopted different positions on offshore processing, but both parties now support the policy despite the United Nations Human Rights Council repeatedly condemning it.
The two major parties have a history of arguing over boat arrivals, but thousands more people come to Australia every year by plane and then overstay their visas.
The latest figures show more than 64,000 people are overstaying their visas across Australia.
The highest number come from Malaysia, followed by China, the United States and Britain.
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