Aussie Prime Minister Scott Morrison has revealed that New Zealand would likely be the first country that Australia would reopen its borders to as it looks to relax Covid-19 restrictions.

This is despite the fact that just a week ago, Morrison said he was not actively considering a change to Australia's border policies.

In a statement to the Herald, a spokesperson for Prime Minister Jacinda Ardern confirmed future border arrangements between New Zealand and Australia had been discussed by the Prime Ministers, but "no plans have been confirmed".

"Our current border restrictions and quarantine arrangements are the most important protections we have to stop the virus re-entering New Zealand and taking off again, so they will only be lifted when we are confident it is safe to do so," the spokesman said.

"So while nothing is going to happen immediately, the idea has merit as something that might be possible down the track."

According to the Sydney Morning Herald, Morrison has had discussions with Ardern about the border reopening.

"I would have thought New Zealand would be the obvious candidate [for border openings] and that's the nature of discussions we've had," Morrison said.

"That is an area we can look potentially favourably on provided all the other arrangements are in place regarding public safety."

He said this was something both Governments were working through "patiently".

Asked about this last week, Ardern said a trans-Tasman travel bubble free from Covid-19 was part of her "ongoing agenda" with Morrison.

But she did not say whether she had already raised that possibility personally with Morrison.

"Certainly that's started with Singapore, and we do have frequent contact with Australia, and at officials' level I couldn't tell you how far along those have got.

"But they will be a part of my ongoing agenda with PM Morrison," Ardern said on Thursday last week.

"For both of us, I anticipate the border restrictions will be present for a long time, so it becomes whether or not there's anything we can build into those border restrictions that take into account our goals to keep Covid out for both of us."

But when asked about this on Monday, Ardern said that conversation with Morrison "will be a way off".

"With a strategy like ours, we can have no tolerance for someone potentially coming in with Covid-19 and setting off a chain of events that could be devastating," she said.

The Prime Minister's office has been approached for comment.

Foreign Affairs Minister Winston Peters has previously suggested New Zealand might open its borders to Australia sooner than the rest of the world if both countries continued to successfully manage the pandemic.

"Our figures with Australia, it's almost as if we've got a trans-Tasman bubble between our two countries, and if the figures keep on going that way, then that is a serious possibility," he said.

Victorian Chief Health Officer Brett Sutton has said eliminating coronavirus across Australia is possible, as new cases in Victoria could drop to zero in coming months.

"Elimination is actually a viable option for us here in Australia so I wouldn't rule it out, in terms of being in as optimistic a position as New Zealand," he told ABC Radio Melbourne yesterday.

• Covid19.govt.nz: The Government's official Covid-19 advisory website