The airline said in a statement it's in discussions with "interested parties" about a sale.
A person with knowledge of the possible deal told The Associated Press that Atlanta-based Delta Air Lines Inc. is in talks with Singapore Airlines about buying the Virgin Atlantic stake. The person requested anonymity because the talks are ongoing.
Virgin Atlantic is the second-biggest airline at London's Heathrow airport, behind British Airways and BA is a partner with Delta competitor American Airlines. Takeoff and landing rights there are limited, a barrier for airlines that want to add flights.
A Delta partnership with Virgin Atlantic on U.S.-London routes would allow it to benefit from Virgin's established position at Heathrow.
Some 51 percent of Virgin Atlantic, which was founded in 1984, is owned by Branson's Virgin Group. Singapore Airlines bought its stake from Branson in early 2000 for 600.3 million British pounds.
Singapore Airlines said in its statement that the talks may or may not result in a deal.
AP Airlines Writer Joshua Freed in Minneapolis contributed.