The leaders held bilateral talks in Sydney today and Ms Ardern reiterated New Zealand's offer made in 2013, which has been rejected by subsequently by successive Australian governments under Labor and the Liberal Party.
Coalition partner NZ First plans to reopen trade negotiations with Russian Federation but Ms Ardern says a new TPP deal tops her agenda.
"What we are seeking to do is ensure there are opportunities for resettlement for the people on Manus Island and Nauru", he said.
Mr Turnbull said his government was focused on a United States resettlement deal to take up to 1250 people.
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.
"We have an arrangement with the United States where a substantial number - 1,250 - can, subject to the USA rigours vetting, be resettled in the United States".
The other 10 countries would remain a matter for negotiations, but she said New Zealand was not the only one concerned.
Sprint and T-Mobile abandon merger talks
It comes as Sprint has somewhat struggled in an increasingly competitive USA mobile market. The two mobile companies have been dancing around a possible merger for years.
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".
Ardern had said she could not ignore "the human face" of what Australia was dealing with.
Opposition leader Bill Shorten has urged Turnbull to take up the deal, saying that it would not put "people smugglers back in business".
Australia withdrew from the Manus Island centre on Tuesday, following a PNG court ruling that the centre was unconstitutional.
More than 600 refugees have barricaded themselves on Manus Island.
"We should give consideration to what New Zealand is offering", former immigration minister Kevin Andrews told Sky News on Sunday.
The stand-off at the Manus Island detention centre prompted Opposition Leader Bill Shorten to issue a statement on Friday, calling on Mr Turnbull to accept the offer, describing it as not dissimilar to the U.S. deal.