New Zealanders have enjoyed a travel bubble with Eastern Australian states since last year that does away with 4-day quarantine, but NZ is yet to reciprocate.

"We are working with Singapore at the moment, potentially for a bubble in July," Mr McCormack, who is also transport minister, told the ABC's Insiders program

"As the vaccine rolls out not only in Australia but in other countries, we will reopen more bubbles."

According to Nine newspapers, Australians would be allowed to travel to Singapore without approval from the Department of Home Affairs, provided they have been vaccinated for coronavirus.

Singaporeans who have had the the jab would be able to travel to Australia without having to complete two weeks of hotel quarantine.

It may also be possible for people from other countries to enter Australia via Singapore after completing quarantine in the Southeast Asian city-state.

However, Prime Minister Jacinda Ardern has yet to allow Australians to freely travel to NZ, frustrated with Australian states flicking the switch from open borders, or 'green zone', to closed, or 'red zone', on short notice in response to NZ COVID-19 outbreaks.

From that frustration, it appears the two countries are no longer attempting to work together on bubble arrangements.

New Zealand's COVID-19 Minister Chris Hipkins says a goal of shared plans between the two countries has all but been abandoned.

However Prime Minister Scott Morrison says he would happily open Australia's borders to Kiwis when Ms Ardern chooses to.

Australian Associated Press