$300 million to $500 million, a person familiar with the negotiations told The Associated Press on Monday.
The person spoke on condition of anonymity because a deal has not been announced.
Singapore Airlines owns a 49 percent stake in Virgin Atlantic. Last week, it said it was in talks with a possible buyer for that stake. Delta has been widely reported to be on the other side of those talks.
It's not yet clear exactly what Delta would do with its stake, but Virgin Atlantic is the second-biggest airline at London's Heathrow airport, behind British Airways.
A partnership with Virgin Atlantic would give Delta access either to some of its landing rights, or at least to some of the financial benefits of flying people to London, whether they're on a plane flown by Delta or Virgin Atlantic.
Landing rights are limited at Heathrow, so airlines can't just add more flights there whenever they want. And currently Atlanta-based Delta has fewer flights from the New York area to Heathrow than either American or United, its main U.S. competitors.
"We believe that if Delta were to acquire these slots it would put it on an even footing with American ... and United" at Heathrow, airline analyst Ray Neidl wrote in a Dec. 3 note examining the implications of such a deal.
When news of the discussions first surfaced earlier this month, Air France — a partner of Delta's on trans-Atlantic flights — was thought to be interested. However, on Monday it issued a statement saying, "Air France-KLM is not involved in current negotiations between Delta and Singapore."
Virgin Atlantic was founded in 1984, and 51 percent is owned by Sir Richard Branson's Virgin Group. In 2000, Branson sold a piece of it to Singapore Airlines for 600.3 million pounds, about $960 million at the time.
Virgin Atlantic has struggled with losses and said in 2010 that it might be interested in some kind of tie-up with another airline. British media reports at that time said that Delta was interested.