Australia's government says it is in talks with several nations about quarantine-free travel, but warns that Europe and the US will not be on the list.
The first agreement would be with New Zealand, Prime Minister Scott Morrison said.
Other nations that could follow suit are Japan, Singapore, South Korea and Pacific Island nations.
Australia closed its borders in March, early into the pandemic.
To date, it has recorded 27,263 cases and 898 deaths.
It has fared better than other nations but recently saw a second wave in the state of Victoria, forcing Melbourne and its surrounding areas into another lockdown. Infections have fallen dramatically since.
From Friday, New Zealanders will be able to travel to some Australian states - New South Wales, Canberra and the Northern Territory - without having to quarantine. But they will have to quarantine in a hotel upon their return home.
On Sunday, one person in a quarantine hotel in Auckland tested positive for the virus. Four cases were reported on Saturday, all imported.
Australians are not yet allowed to travel to New Zealand.
Mr Morrison said he had spoken about travel bubbles with his counterparts in Japan, South Korea and some Pacific nations, while Foreign Minister Marise Payne held talks in Singapore.
"But we have to go cautiously on this - very very cautiously. Covid-19 hasn't gone anywhere. It's still there. And no less aggressive today than it was six months ago," Mr Morrison said.
It came as Tourism Minister Simon Birmingham warned that travel to high-risk areas such as the US and Europe was unlikely to happen until late 2021.
"The prospects of opening up widespread travel with higher risk countries will remain very reliant on effective vaccination or other major breakthroughs in the management of Covid," he said.
What is the latest in Australia?
Melbourne has been easing its lockdown for the past several weeks following a decline in cases. It had been hoped that all shops in Melbourne would be allowed to open and outdoor dining would resume by 19 October.
But Victoria's Premier Daniel Andrews says the number of new cases is not yet falling fast enough to ease all of the restrictions that were promised. On Sunday, 12 infections and one death were reported in the state.
Queensland's border with New South Wales is still yet to open.
Queensland's government said on Friday it would make a decision on re-opening the border at the end of this month. As of Friday, the state had reached 28 days without community transmission.
Western Australia's borders are closed to the rest of Australia. The government there has said it may not reopen its borders until April, according to local media.