Hunt said he was "optimistic" a vaccine was close, but declined to confirm details in the report.
He said the Australian government has signed two nondisclosure agreements related to the production of a vaccine.
"We are in advanced negotiations with a range of different companies with regards to a vaccine," Hunt told Sky News on Sunday morning.
"I am now on the basis of our best advice genuinely more optimistic.
"I think the work is moving closer to a vaccine."
While optimistic, Hunt said it was still most likely a vaccine would be available next year at the earliest.
"It anything happens before then, then that would be an outstanding result, not just for Australia but for the world," he said.
He said the negotiations provided a "genuine ray of hope".
"We're advanced, we're prepared and we're in a position to produce," Hunt said.
His comments come after Mexico and Argentina reached agreements to produce the Covid-19 vaccine designed by Oxford University.
Last week, former chief medical officer Brendan Murphy confirmed Australia was exploring its options for a vaccine, saying once a deal was locked in it would take just weeks to begin production.
"We have been closely following all of the vaccine developments, we are actively discussing with all of the so far successful candidates, we are not at the back of the queue," Murphy said.
"There will be further announcements shortly.
"We are well in front of the queue."
