She said the Government was working to remove the investor-state dispute settlement provisions from the deal that allow corporations to take legal action against a foreign government for introducing legislation that harms their investment or profits.
The meeting comes as roughly 600 asylum seekers on Manus Island have been left without power, food and water in an attempt by the government to encourage them to seek refuge on the island proper.
While opposition leader Bill Shorten's Labor predecessors Kevin Rudd and Gillard also declined to accept New Zealand's offer, he spoke in favour of the deal on Friday.
"What we are seeking to do is ensure there are opportunities for resettlement for the people on Manus Island and Nauru", he said.
The offer, first made by the country to the Gillard government in 2013, has been rejected a few times on the grounds that it would give asylum seekers a backdoor into Australia and become a marketing opportunity for people smugglers.
"In the wake of that obviously we can consider other ones", he said.
Asked at her post-Cabinet press conference this afternoon if she's interested in meeting Mr Putin at APEC, Ms Ardern said she has to "prioritise those elements of our trade agenda which are acute".
"We of course do not have the circumstances that Australia is operating under, but we also can not ignore the human face of what Australia is dealing with".
Mr Thomas also said the PNG government could not continue to bear the cost of watching over residents at the mothballed centre.
"I don't want to give away too much of that conversation but it's fair to say a number of states speaking more broadly have taken issue with ISDS clauses", Ms Ardern said on Sunday.
"The reality is, we have an intractable problem at the present time", he told Sky News.
Mr Turnbull's decision not to accept the offer may prolong what Greens leader Richard Di Natale has called a "humanitarian catastrophe" on Manus Island.