Talks between Singapore and Australia about a travel bubble have begun after the city-state announced it would allow entry from all states and territories excluding Victoria from next week.
But it won't be an immediate priority for Australia.
Singapore's Transport Minister Ong Ye Kung said in a Facebook post on Thursday he had spoken with his Australian counterpart, Michael McCormack, about the move.
"Like Brunei and New Zealand, Vietnam and Australia have also very successfully controlled the spread of the COVID-19 virus," he said.
"We will hence lift border restrictions for visitors from Vietnam and Australia (excluding Victoria)."
He said visitors would have to apply for an air travel pass and undergo a COVID-19 test upon arrival, with those registering a negative result not required to serve a "stay-home notice".
"I spoke to Mr Michael McCormack ... (and his Vietnamese counterpart) earlier today. They were appreciative of Singapore's decision and when conditions are right, I believe they will consider reciprocating the lifting of restrictions to travellers from Singapore."
ACT Chief Minister Andrew Barr told AAP he would support a travel bubble between Canberra and Singapore.
"Yes, provided all of the COVID-safe protocols are in place," Mr Barr said on Thursday.
A month ago, Singapore lifted its border restrictions to allow visitors from Brunei and New Zealand.
Since then 136 visitors have entered Singapore, all of whom have tested negative upon arrival.
At present, Australians are not allowed to travel overseas unless the traveller has an exemption from the Department of Home Affairs.
There are also caps on the number of passengers coming into Australian airports from overseas.
A spokesman for Prime Minister Scott Morrison told AAP the government's immediate priorities were on bringing vulnerable Australians home and finalising arrangements with New Zealand.
"As further opportunities with other nations arise, we will seek to pursue them in the same way as we are with New Zealand, guided by appropriate health advice," the spokesman said.