Scott Morrison hopes to be able open up Australia's international border to tourists soon after the success of partial openings to students, backpackers and skilled migrants.
The prime minister said many of the states have now passed their peaks in COVID-19 infections.
"The key issue that we have been examining and I have asked for advice from our health officials now over recent weeks, is how that decision could impact on our hospitals, which has been our primary consideration," he told reporters in Sydney on Sunday.
"But I really do not believe that is far away. As people will know, we have already opened up our borders to skilled migrants and backpackers and students."
Home Affairs Minister Karen Andrews was slightly more cautious on the timing.
"We don't have all of the information that we need to be able to take the decision to open, but we are very close," Ms Andrews told ABC's Insiders program.
Neither would she guarantee that once open, borders would stay open.
"We don't know what might be coming our way. No government does," she said.
Labor's home affairs spokeswoman Kristina Keneally said the lack of information about an upcoming change to the borders was concerning.
"Any effort to provide Australian families and businesses more certainty is welcome after two years of border chaos and Mr Morrison outsourcing border decisions to the states," Senator Keneally said.
"Until Mr Morrison stops constantly prioritising headlines over developing a clear and safe plan to reopen our borders, Australian families and businesses won't be able to plan for a better future."
Such discussions came as NSW posted 7893 COVID-19 cases and a further 28 virus-related deaths.
NSW announced new support measure for businesses hit by school virus safety measures in late 2021.
Treasurer Matt Kean said businesses such as overnight camp and music education providers will now have access to a $14 million grant program.
"The grants will provide eligible businesses and not-for-profit organisations one-off payments equal to 40 per cent of their decline in Term 4 2021 turnover compared to previous years, up to $15,000," Mr Kean said.
There were 7169 new infections in Victoria and six deaths, while Queensland recorded 5746 and nine deaths.
Queensland Deputy Premier Steven Miles says seven of the nine deaths were aged care residents and only four of the dead had received two doses of a vaccine, and none had had a booster.
Federal Labor's health spokesman Mark Butler said there is a full blown crisis in aged care
"Tens of thousands of older Australians locked in their room isolated from each other, from their family and visitors. And most tragically, more than 600 older Australians losing their lives to COVID in aged care in just the five weeks just gone by," he told reporters in Adelaide.
"The government needs to fix its debacle of a booster rollout in aged care, 60,000 aged care residents at least still not boosted and 60 per cent of aged care staff still not with a booster shot."
In Tasmania there were 471 cases and one death, while the ACT reported 323 cases.
