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.