Australia is refusing to take any of those in the camp and about 600 are refusing to leave and remain at the centre without food, power or other facilities.
Greg Barns, a lawyer for refugees and asylum seekers on Manus Island, said it provided Ardern with a chance to stamp her mark.
Papua New Guinea and New Zealand should bypass Australia and come to an agreement for New Zealand to take the refugees, he said.
Barns pointed to former Prime Minister Helen Clark's decision to accept about 130 of the refugees from the ship The Tampa - an act Clark has often said was one of the proudest moments of her leadership.
"Helen Clark did the right thing and it would be great if Jacinda Ardern did the same. It's a chance for New Zealand to show moral leadership, which Australia has lacked now for 20 years."
Ardern will repeat New Zealand's standing offer to take 150 from Manus Island and Nauru once they had gone through the screening to ensure they were genuine refugees - an offer in place since 2013 but which Australia has repeatedly refused, saying it would provide incentives for people-smugglers.
She acknowledged New Zealand did not have to deal with issues such as people-smugglers and boat people as Australia did.
"But it is hard to ignore the human face of this situation and nor should it be ignored."
Ardern said she had not yet considered whether she would pursue it without Australia's say so and would wait to see how Turnbull responded.
"They have chosen a particular strategy to manage the issue of boat people and the significant threat that attempting to get to Australia poses on those people's lives. All I can do is address it from New Zealand's perspective and New Zealand's international obligations."
Australia had agreed to New Zealand taking the Tampa refugees - but Barns said if Australia did not agree to Manus Island, New Zealand and PNG should be able to enter an arrangement without Australia's interference.
"They should not feel the need to talk to the bully boy in the region.
"New Zealand has a much better track record on human rights internationally than Australia and it's an opportunity for this new Prime Minister to stamp her mark on the global stage as a country which takes human rights seriously."
When former Prime Minister John Key last made the offer last February to take 150 refugees, Turnbull knocked it back saying it would be seen as a "marketing opportunity" for people-smugglers.
There were also concerns the refugees would use New Zealand as a back door to Australia because of the freedom of movement between the two countries.
National Party Foreign Affairs Spokesman Gerry Brownlee said there would be risks in going ahead against Australia's wishes.
"There were occasions where there were boats allegedly on the way to New Zealand and for us to do anything about that, we would require a fair bit of co-operation with the Australians. So we need to stay pretty lock-step with Australia in the way they are dealing with this problem."
He said it was easy to talk about dealing directly with PNG: "but it would be unfortunate if we got out of lock-step with Australia on this."
"Nobody likes to see those people on Manus Island with their lives very disrupted, but you've got to remember it wasn't Australia or New Zealand that disrupted those lives in the first place."
Asked if she believed New Zealand was a target for people-smugglers, Ardern said "a very difficult one".
"Our job is to tackle the issue we have here and now. The offer has been made and we'll work through that on Sunday."
Green Party refugee spokeswoman Golriz Ghahraman also believed Ardern could make the offer straight to PNG rather than Australia if she could not get Turnbull to agree.
"If we can invest in this, and take the 600 it would be a real Tampa moment for New Zealand. Helen Clark captured the essence of the Kiwi identity when she took in the Tampa refugees that Australia was about to leave to drown."
Barns also said he hoped Ardern would raise the plight of the so-called 501s - those being deported to New Zealand after a policy change which meant anyone who had served more than a year in prison would be deported, regardless of how long they had lived in Australia.
There are still 178 New Zealanders in detention centres in Australia under those provisions awaiting appeals or deportation.
