Australia may add more countries to its travel bubble, and Singapore is reportedly at the top of its list.

A decision to open the country up to more destinations comes as Australia lifted mandatory quarantines for travelers coming from New Zealand.

Australia's Deputy Prime Minister and Minister for Transport, Michael McCormack, said Thursday that they have come up with a list of countries that will eventually be included in the next bubble, adding Singapore is at the top.

McCormack said the government is looking for countries that have the lowest COVID-19 transmission risks. He said officials have already begun talks with Singapore's transport ministry for implementing a travel bubble.

"Hopefully more travel bubbles will be able to be opened up with perhaps Singapore, (and) who knows, Japan, South Korea, South Pacific island nations," McCormack said.

During the pandemic, Australia imposed one of the world's strictest travel restrictions, completely locking down the nation from all incoming and outgoing travel. Thanks to its swift action, Australia quickly reduced its daily transmission numbers.

In recent months, the nation has mostly been COVID-19 free, with only a handful of occasional local outbreaks. Earlier in the week, the government finally allowed quarantine-free travel to and from the county and New Zealand. The opening of the travel bubble led to hundreds of tearful reunions and an overall positive outlook for both nations' tourism recovery.

 Qantas chief executive Alan Joyce said he hopes Australia will open travel bubbles to more destinations soon.

"Of course, we would like to see the rest of the international borders open up. But we want it to happen in a safe way because we don't want all of the good work that has happened in the domestic market to go backwards ... when you have any form of quarantine, it does suppress demand for travel," Joyce said.

Australian Prime Minister Scott Morrison echoed the sentiment and made it clear that he will not rush the nation's reopening. Morrison said the pandemic was still raging in some parts of the world and he doesn't want to take any unnecessary risk.