If approved by the Therapeutic Goods Administration (TGA)'s vaccine advisory committee, some frontline healthcare workers and aged care residents could start receiving their third doses, reports Xinhua news agency.
"We're in a position that if, by the middle of next week, there is an approval for a third dose of Pfizer, then we would be able to begin immediately," Hunt said.
Experts have recommended that Australians have their third vaccination dose six months after their second.
Brendan Murphy, the secretary of the Department of Health, said there is no evidence that vaccine protection against severe disease wanes after six months but that booster shots could "give people the best additional belt-and-braces protection".
"Antibody levels are only part of the protection of vaccines," he said.
"When you get the infection, if you've got what we call immune memory, even if your antibody levels have fallen, the cells are still there to make antibodies again. If the virus infects you, you will mount an immediate antibody immune response and that is what protects you."
On Saturday, Australia reported more than 2,100 new locally-acquired Covid-19 cases and 11 deaths as the country continues to battle the third wave of the pandemic.
Since the onset of the pandemic in early 2020, Australia has reported a total of 158,604 confirmed Covid-19 cases, with 1,637 deaths.
So far about 86.4 per cent of Australians aged 16 and over have received one Covid vaccine dose and 72.5 per cent are fully inoculated, according to the latest data released by the Department of Health.