"The most likely scenario is Air NZ and Singapore teaming up to take Virgin private and acquiring Branson's stake," the AFR said.
Air New Zealand bought into Virgin to gain exposure to large domestic market and help rationalise transtasman operations where competition is cut-throat.
Luxon said his airline's stance was confirmed with the board last month.
"Virgin Australia has an excellent strategy being delivered by a top chief executive (former Qantas executive John Borghetti), who intimately knows his market place and the opportunities to seize."
Luxon said he was not surprised that Etihad and Singapore Airlines had seen the same potential in Virgin Australia and have been progressively lifting their interest in the airline.
"All shareholding airlines are strong and logical partners. Air New Zealand enjoys good relationships with both Etihad and Singapore Airlines, including at CEO level."
He said he was confident Virgin would continue to attract more share of both business and leisure customers.
In a Business Herald Meet the CEOs interview Luxon said his airline's shareholding of between 20 per cent and 26 per cent "is where we want to be."
Its partnership with Virgin meant it could directly link 26 centres in New Zealand with 25 in Australia.
'It's about finding an efficient way to get access and exposure to a domestic Australian market that's large, adjacent to New Zealand, growing and rather connected. Setting up our own airline within that construct in the Australian domestic market would not be a profitable or efficient way of doing it."
Air New Zealand had a stake of about $300 million in Virgin which was manageable given it had about $1.2 billion of cash in the bank, Luxon said.