Mr Morrison was speaking in Cairns, where he was announcing a A$60m () package aimed at stimulating tourism to the regions of the country hit hardest by the pandemic travel slump.
“In the very near future the health minister will be making some further announcements about things, particularly involving pre-testing of flights for those getting on flights to come to Australia,” said Mr Morrison.
“That will be an important milestone that’s not too far away from us now.”
At present, all international visitors need to take a PCR test within the 72 hours before departure, or an antigen test no more than 24 hours prior to travel.
Fully vaccinated foreign visitors can enter Australia, while unvaccinated travellers still need a special exemption in order to go.
Mr Morrison told the Cairns event that the new package was all about getting international travellers on inbound flights.
“As the world reopens, and travellers get out and see the world again, we want to ensure that at the top of every must-see-list is Australia,” he said.
“I have been listening to tourism industry operators about what they will need to rebuild their international tourist businesses and this funding boost will deliver on these needs.
“The return of our international tourism market will support hundreds of thousands of tourism jobs, strengthen our economy, and back our world-class tourism operators and the many regions reliant on international visitors, like tropical North Queensland.”
Some A$15m of the government package will go to Tourism Tropical North Queensland to be spent on promoting the region and the Great Barrier Reef to international tourists.
Meanwhile, A$45m will be allocated to nationwide organisation Tourism Australia for targeted campaigns to get tourists back into areas deprived of spend during the pandemic.