Health Minister Chris Hipkins says the Government is looking at countries that Kiwis would be able to travel to despite the ongoing pandemic, without having to isolate on return.
Hipkins told Morning Report the areas with no community transmission of the disease could be designated a safe travel zone.
"Australia obviously has some states which are in that position, [there are] a lot of countries in the Pacific which are in that position."
There is also ongoing work to look into what to do with people who arrive from countries with large Covid-19 outbreaks.
Ten cases were picked up in managed isolation last week, all linked to a single flight from India.
On Tuesday, the Prime Minister told Morning Report people returning from countries deemed high risk may soon have extra precautions.
Hipkins said on Thursday the government is looking into what to do once people leave isolation.
"One of the things that the technical advisory group, so this is all the scientists and you know the experts, are looking at at the moment, is whether there should as an extra safeguard be some follow up after that 14 days.
"So that's a week after you leave quarantine should you then have another test just to make sure that you're not in a very, very small minority of people who can potentially cultivate it for more than 14 days."