The pair had previously visited the nation in 2018 at the end of a 16-day royal tour of the South Pacific.
Governor-general Dame Patsy met the couple during their travels.
“I remember they’d just been down to the Abel Tasman National Park when we sat down and had a drink, and they said that they could imagine living in a place like this and wondered whether we thought it would be theoretically possible.
“Even possible for them to have a place in New Zealand,” she told the Associated Press.
Dame Patsy said she told the pair: “It would be fine. There are lots of opportunities to live in New Zealand, but that would be something that they’d have to explore.
“They were looking at how they might raise their family. And obviously they’ve made some decisions since.”
But she added that she did not see it as a formal request for assistance but more of an informal discussion about the couple’s hopes for the future.
The news comes just months before Dame Patsy, 67, leaves her largely ceremonial role representing the Queen in New Zealand in October after a five-year term.
Her role consists of officially signing bills into law, presiding over public ceremonies and tours the country, meeting various groups.