Virgin will form a joint venture with Delta if the U.S. carrier buys Singapore Airlines' 49 per cent stake in the UK airline.
The source said Virgin founder Richard Branson was not immediately looking to sell any of his 51 per cent stake in the UK airline and was "concentrating on working with Delta" which is closing in on agreeing a deal to buy Singapore's stake.
Delta and Virgin plan to set up a revenue-sharing deal on flights between Britain and the U.S., which would involve a code-share agreement, allowing both to sell flights on the other airline and share revenues from ticket sales, the source said.
The joint venture could eventually lead to the pair sharing costs and bringing their prices and schedules into line, the source added.
The partnership would be similar to that operated by IAG's British Airways (BA) and American Airlines since 2010 on all transatlantic flights on routes between the U.S., Canada and Mexico and many European routes.
Airlines like Delta have long hoped to break into London's capacity-constrained Heathrow airport, a lucrative hub for corporate passengers where landing slots are generally hard to acquire.
Virgin Atlantic is the second-largest carrier at Heathrow after BA.
A combination with Delta, the second-largest U.S. airline by revenue after United Continental, would be a shot in the arm for Virgin.
The British carrier has been battered by rising fuel prices and the euro zone crisis, and posted a loss of around £80 million in its last full year.
Singapore and Delta are still in talks over the sale of the stake, which the Asian carrier bought for £600 million in 1999, but now wants to sell to refocus on its key markets.
Weekend reports in the British press said Air France-KLM, which also has a partnership with Delta on some transatlantic routes, was in talks to buy part of Branson's stake - a deal which would effectively give Delta and Air France-KLM control over Virgin Atlantic.
However, Branson is unlikely to sell down his stake in the near future, the source added.
Branson, who set up Virgin Atlantic in 1984, has been weighing the airline's future for years and two years ago appointed Deutsche Bank to examine offers.
Earlier this month sources told Reuters that Delta was keen to see Air France-KLM - a member of its SkyTeam alliance - buy a stake in Virgin to give the pair control of the British airline's operations.
The European Union requires that EU carriers be under European control, meaning Delta would need an EU airline as a partner if it wanted majority control of Virgin Atlantic.
If Air France-KLM were to buy a small percentage of Branson's stake, then Virgin Atlantic could continue to be European controlled.