LONDON — Delta Air Lines expand at London’s Heathrow airport, Europe’s busiest, if it succeeds in buying the 49 percent stake of Virgin Atlantic Airways Ltd. that’s held by Singapore Airlines Ltd.

Talks are under way between Delta and Singapore Airlines, two people familiar with the matter said. A stake sale could let Virgin form a trans-Atlantic venture with Delta and partner Air France-KLM Group in the SkyTeam alliance, providing access to takeoff and landing slots at the British carrier’s Heathrow base.

“Delta doesn’t have that many flights to Heathrow, and Virgin would get more access” to airports in New York and Los Angeles via Delta, said Jeff Straebler, an analyst with John Hancock Financial Services in Boston. “In terms of having a presence at Heathrow, it’s the only way for Delta.”

Delta, Air France-KLM and their SkyTeam partners are the smallest alliance group at Heathrow, with about 5 percent of slots. Oneworld, led by British Airways and AMR Corp.’s American Airlines, dominates with almost half of all service, followed by United Continental Holdings and its Star Alliance with about a quarter of slots.

Delta, he world’s second biggest airline and the largest serving Charleston International Airport, is discussing buying all or part of the Singapore Airlines stake, said the people familiar with the discussions, who asked not to be identified as the matter is private.

Paris-based Air France-KLM, Europe’s largest carrier, might also purchase stock, they said.

“We view Delta as a smart strategic buyer that will not overpay for any asset,” Vicki Bryan, an analyst at New York- based debt researcher Gimme Credit LLC, wrote Monday in a note to clients.

Singapore Air paid 600.3 million pounds for the Virgin stake in 1999, or about $961 million today. Delta may pay $1.1 billion to $1.3 billion for the stake, CNBC reported, citing sources it didn’t identify.

A Virgin Atlantic deal would be Delta’s third with a foreign carrier in recent years. Atlanta-based Delta agreed to buy 3 percent of Brazil’s Gol Linhas Aereas Inteligentes for $100 million in 2011, and completed a $65 million investment in Grupo Aeromexico SAB this year after a regulatory review. Both deals also gave Delta a board seat.

Regulators probably would approve an agreement between Delta and Virgin Atlantic because competing groups already are so much bigger, Straebler said. European Union rules require the zone’s airlines to be under European control.

“Delta would have the least challenge in getting it approved, and the most benefit in doing it,” he said.

Spokesmen for Delta, Virgin and Air France-KLM declined to comment. Negotiations with “interested parties” may not result in a transaction, Singapore Airlines said in its statement.

The North Atlantic travel market is the world’s biggest for first- and business-class flights, according to the International Air Transport Association trade group. Slots at Heathrow, the world’s third busiest airport, are so prized that Continental Airlines paid $209 million for four pairs in 2008.

That was the year when new EU rules allowed Delta and most U.S. competitors to start serving Heathrow, the preferred airport for London business fliers because it’s only about 15 miles (24 kilometers) west of the capital. Gatwick airport, Delta’s previous London base, is 28 miles south of the city.

Richard Branson, Virgin Atlantic’s billionaire founder and the holder of a 51 percent stake, probably would remain in control of Crawley, England-based Virgin, Chief Executive Officer Steve Ridgway said in an interview.

“He is the majority shareholder,” Ridgway said.

Virgin Atlantic has rejected the global alliances for a decade. The groups allow carriers to book passengers on one another’s planes, in effect expanding their networks without the cost of additional planes and crew.

Some carriers such as Delta and Air France-KLM have an even deeper relationship with antitrust immunity that lets them coordinate fares and flight times and operate as a single entity. European and U.S. laws prevent foreign carriers from owning a majority stake in an airline.

“Virgin has rather lost its way as the world consolidates and they really need to bite the bullet,” said John Strickland, director of JLS Consulting in London. “Signing up to SkyTeam would be part of it, I’m sure, and they could bring a rock solid basis to Delta’s trans-Atlantic alliance with Air France-KLM.”

Branson said last month that he’s seeking an alliance for Virgin Atlantic, which faces pressure from fuel prices and an American-British Airways joint venture at Heathrow. He lobbied regulators for more than a decade to try to block the tie-up.

Virgin Atlantic hired Deutsche Bank to assess options in 2010. The carrier posted a pretax loss of 80.2 million pounds for the year ended February.

Branson also is seeking a successor to Ridgway, 61, who retires next year after 11 years as CEO. During his tenure the carrier has emphasized perks such as spa treatments and high- design lounges to win high-end travelers.

Virgin is “well down the road” in choosing a new chief, Ridgway said in the interview, adding that the aim is to make an announcement before Christmas and that candidates won’t be put off by the likelihood of a new investor.

Singapore Airlines is looking to sever ties with Virgin Atlantic to focus on local markets at the same time that Gulf carriers Emirates, Qatar Airways Ltd. and Etihad Airways present new challenges, Ridgway said.

“India has opened up, China has opened up and there are three fearsome competitors on their western side,” he said. “That’s what their agenda is about.”

Mathieu Rosemain, Patricia Kuo and David Fickling contributed to this report.