In November, Virgin Atlantic hired Deutsche Bank to examine the aviation market and the airline's position within it.
Virgin Atlantic is believed to have been approached since by a series of other airlines about a deal, but according to reports, Branson would need to sell his majority stake in order for them to take an interest.
Branson owns a 51% stake in Virgin Atlantic, which he founded in 1984, while Singapore Airlines owns the remaining 49%.
According to reports, the carrier has received a number of inquiries since the investment bank was brought in, a move made soon after transatlantic competitors British Airways, Iberia and American Airlines received clearance to co-operate on transatlantic flights in September.
BA and Iberia had earlier signed a merger agreement.
Branson is reported to be worried that Virgin Atlantic could be left behind while the airline industry continues to consolidate operators, and that he is exploring different strategic options that could lead to joint marketing ventures with rival airlines.
Virgin Atlantic was not available for comment.