This led to Australia seeking a deal with the United States, which agreed to accept 1250 refugees. So far 940 people have been resettled there, while another 258 refugees have been provisionally approved for resettlement but await travel.
On Wednesday, Andrews told The Age she had started talks with her New Zealand counterpart about accepting the offer.
However, she said she had made it "very clear" to New Zealand there wouldn't be a back door method for refugees to be able to return to Australia.
"We're working through those issues now and we will continue to do so, and of course we will continue to work with the United States about resettlement options there as well," Andrews told The Age.
Faafoi said he'd been approached by former Home Affairs Minister Peter Dutton "early this year or late last year" about taking up the offer, and again by Andrews, who took over the role in April, just last week.
"The offer has been there since 2013. It is still open, but there are still details that need to be worked through and bottom lines in that," Faafoi said.
One of those "bottom lines" was ensuring it went through the United Nations High Commissioner for Refugees process, Faafoi said, which guaranteed a pathway to full citizenship and all the rights that entailed.
"If they come to New Zealand it will be under the auspices of the UN programme, eventually becoming citizens. We would want them to have the full rights of New Zealand citizens."
Refugees who arrive in New Zealand under the Refugee Quota Programme are granted Permanent Residence status in New Zealand, meaning they would still need to acquire a visa to travel to Australia.
Most New Zealand citizens can visit, live and work in Australia without applying for a tourist or work visa, however.
Asked about Australia concerns of New Zealand becoming a "back door", Faafoi said that was "their issue".
"Any intention Australia has in that is their decision. We have made it pretty clear on a number of occasions, if they come here, they will eventually become New Zealand citizens, and we would like them to have the full rights of New Zealand citizens."
Faafoi said New Zealand had capacity for the extra 150 refugees, which would be on top of New Zealand's current annual quota of 1500.
However, due to Covid-19 the quota had been greatly reduced. After pausing for much of the pandemic it recently resumed at a reduced level, with 750 to 1000 individuals to be resettled over 2021/2022.
Faafoi denied any deal was about giving New Zealand any sort of human rights PR boost.
"There are some fundamental rights here, the lives of those on PNG and Nauru are not ideal. There have been offers from two different governments, open for some time."
Officials between the two countries would be meeting this month to discuss further details, Faafoi said.