The scheme would not work with the existing 14-day quarantine requirements but the return of Australian visitors would be a boon for this country's hard-hit tourist sector which for now must rely on the domestic market.
Struggling airlines are also eager to resume operations across the Tasman with Air New Zealand and Qantas now flying just a handful of services to repatriate nationals.
As the Government is doing in this country, Birmingham urged Australians to support local tourism operators and had bad news for those wanting to travel overseas.
"I do, sadly, think that in terms of open tourist-related travel in or out of Australia, that remains quite some distance off, just because of the practicalities of the volumes that are involved and the need for us to first and foremost keep putting health first."
In this country, the Opposition says the case of two women coming from Britain and now Covid-19 positive would lead to an inevitable delay.
But on RNZ, Peters said the bubble hasn't been jeopardised after a quarantine blunder allowed the pair to travel out of an isolation hotel.
"These two New Zealanders came out of the UK, a very Covid-troubled country, and we're dealing with Covid safe states," Peters said.
However, National Party leader Todd Muller said while the Government was yet to set clear criteria for when travel between the two countries could resume, the bungled case meant it was not going to happen any time soon.
"It makes the opportunity to connect with Australia further away, the opportunity to connect with international students less likely, and the tens of thousands of New Zealanders whose jobs will be at risk know that to be true."