More than 600 refugees have barricaded themselves in the mothballed detention centre, which closed on Tuesday.
The Prime Minister said Australia has not accepted New Zealand's offer take 150 refugees from Manus Island.
"We should give consideration to what New Zealand is offering," former immigration minister Kevin Andrews told Sky News on Sunday.
"It's a difficult problem but we should not rule out any particular solution."
Today's headlines
Saudi princes, ministers and tycoons arrested in sweeping purge
He acknowledged there were concerns about a New Zealand refugee resettlement deal establishing a pull factor for people making boat journeys or becoming a back door to Australia.
But Mr Andrews said if a deal could be crafted to work around those issues it should be given thorough consideration.
Earlier today, Finance Minister Mathias Cormann has declined to pre-empt the remarks of Mr Turnbull but said it was in Australia's national interest to be tough on people smuggling.
"The last thing we want to get this terrible trade under way again," he told Sky News on Sunday.
Opposition Leader Bill Shorten believes the government should accept the offer.
New Zealand, which takes a total of 750 refugees a year, first made its resettlement offer in 2013, to the then Labor Gillard government.
The offer has been rejected more than once on the grounds it would give asylum seekers a backdoor into Australia and become a marketing opportunity for people smugglers.
Overnight, one refugee was reportedly experiencing heart problems.
Food and drinking water has run out and the group is too scared to move to alternative accommodation in the main township out of fear they'll be attacked by locals.
The last food packs were distributed on Sunday.
Meanwhile, Immigration Minister Peter Dutton has accused the Greens of using the remaining refugees and asylum seekers on Manus Island for their own political ends.
"It's quite distressing to see the Greens ramping up the tempo on Manus Island because I don't want to see any incident there. It's clear the Greens do," Mr Dutton told ABC radio on Sunday.
Greens MP Adam Bandt had labelled Mr Dutton a "terrorist" his handling on the centre's closure.
"If the definition of terror is to use violence and threaten people's lives for political purposes, then Peter Dutton is a terrorist," he told a rally in Melbourne on Saturday.
