The billionaire businessman said in an interview with Your Money that he wants the airline to compete with Qantas on its much-vaunted London-to-Perth route.
The 14,470-kilometre service to Western Australia, the third longest flight in the world, began this year to much fanfare.
Branson told the TV program he wants services to start "as soon as possible".
It is likely the Virgin Atlantic founder, who is no longer on the executive team and has just a 20 per cent stake in the airline, had a keen eye on the prestige garnered by Qantas when it became the first carrier to operate a scheduled passenger flight between the UK and Australia.
Qantas said in August that the route had been a success and was "exceeding expectations", with flights on average 92 per cent full, and 94 per cent in business class.
"Amazing performance for a new operation," said chief executive Alan Joyce.
The airline is plotting direct flights between London and Sydney, on the country's east coast, as part of its Project Sunrise.
Should Virgin, which flies to a score of long-haul destinations, including New York, Hong Kong and Shanghai, decide to fly to Australia, it would be able to link up with its sister airline, Virgin Australia, for dozens of domestic routes and further afield to New Zealand and the Pacific.
'Speaking in an aspirational sense'
Virgin Atlantic's entrance into the so-called "Kangaroo" market might also benefit passengers by driving prices down.
The airline, which has 17 Boeing 787s in its fleet, the same aircraft Qantas uses on its route, previously flew to Sydney via Hong Kong but scrapped the service in 2014.
A Virgin Atlantic spokesperson, however, poured cold water on Branson's ambitions - but not definitively.
"We don't have any plans to launch flights to Perth," the spokesperson said. . "Richard was probably speaking in an aspirational sense.
"Although our current fleet doesn't have the right configuration for this route, we are always evaluating new destinations for our customers - and Perth is a great city."
Branson's interest in flying to Australia comes amid a surge of innovation in ultra-long-haul flights.
This month, Singapore Airlines launched the world's longest flight, linking Singapore with New York with a 9534-mile, 19-hour service.
The route was the culmination of years of work with aircraft manufacturer Airbus to ensure its Airbus A350-900ULR could complete the trip in a financially viable way.
Boeing, whose aircraft fly the London to Perth route, is planning a response to the Airbus plane, in the form of the 777x, a long-range aircraft due to enter service late next year.
Virgin does not as-yet have orders for either the 777x or the A350-900ULR on its books, but instead has announced its intention to buy 12 A350-1000s to replace its ageing 747s.