He said the topic was something his medical expert panel was “working on right now”.
“I think that is the next step, but I do think that next step is some way away,” Mr Morrison told 3AW.
“If you’re fully vaccinated, that you would be able to travel, certainly around Australia, but maybe overseas, without the need for hotel quarantine.”
He would also need to be satisfied that people could reliably isolate at home.
Vaccines are now available to people older than 50.
So far, 2.4 million people have got a coronavirus vaccine first-shot in Australia.
Meanwhile, the India travel suspension is “looking good” to end on May 15 as scheduled.
Mr Morrison reiterated that the “pause” was always a temporary arrangement.
“I can tell you the pause is working. It was the right decision for Australia’s health and safety,” he said.
“I’m very confident that after the 15th of May, those repatriation flights are able to be restored.”
Since the ban was put in place, hundreds of people in Australia have applied to go to India.
“All of those have been rejected,” Mr Morrison said.
The Prime Minister defended himself against criticism levelled at him by former cricketer Michael Slater.
But the Prime Minister stood firm in his call to suspend flights coming in from India.
“I understand that he’s upset. I understand he’s frustrated. I understand that many people are,” he said.
“I understand the deep feeling. But as Prime Minister I have to make decisions in the national interest.
“We have to be very cautious. I accept that this is a very cautious decision, but cautious decisions have been very effective for us.”
Many of Australia’s most prominent cricketers are currently stranded in India following the travel ban.
This content first appear on 9news