Qantas plans to order aircraft capable of making the 20-hour flight between London and Sydney.
Chief executive Alan Joyce told the BBC he was in advanced discussions with Airbus and Boeing over a potential order next year.
Flights could start around 2022 if the right aircraft was produced, he said.
Qantas also plans to fly non-stop from Australia to North America – slightly shorter than the London-Sydney non-stop flight.
Joyce told the BBC’s Today Programme he was confident there would be demand for the flight.
“Business traffic and general leisure customers would rather have the certainty of getting there direct, not having to stop, not having connections gone wrong, the extra speed that that entails is really important,” he said.
The airline started a non-stop Boeing 787 Dreamliner service between London and Perth in March with flights taking just over 17 hours.
The flights had been 92% full on average, with business class even higher at 94%.
But there was no aircraft yet that could handle the longer London-Sydney flight.
Qantas is considering the Airbus A350-1000 for the service but the long range aircraft would require “modification” because it “needs a little bit more range to get there”.
The Boeing 777-8, a new version of the 777, which is expected to be ready in 2022, is also under consideration.
If the non-stop flights – dubbed Project Sunrise – go ahead, Joyce said the airline would also start flying non-stop to New York as well.
“Qantas is unique because we can probably justify a large number of these long haul aircraft, given how far Australia is from the rest of the world,” he said.
Singapore Airlines launches non-stop flights next month from Singapore to Newark, New Jersey – a journey that will take nearly 19 hours.
Qatar Airways currently offers the longest non-stop flight available – an Auckland to Doha route which takes 17.5 hours.
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