Tony Fernandes, who runs Asia's largest budget carrier by fleet size, is understood to have renewed his interest in the UK airline after previously considering and deciding against a bid.
Any deal could be worth up to 1bn.
Billionaire Sir Richard Branson has a 51 per cent stake in the airline he founded in 1984. Singapore Airlines paid 600m for a 49 per cent stake in Virgin Atlantic in 2000.
The UK airline said earlier this month it had received several "lines of enquiry" about tie-ups with rivals after it hired Deutsche Bank to assess the aviation market.