The balance of power in the London Heathrow long-haul market may once again shift, as the Virgin Group and Singapore Airlines (SIA) appear to be moving closer to selling a stake in Virgin Atlantic, possibly to Delta Air Lines and Air France-KLM.

SIA in a short statement to the Singapore stock exchange says it is “in discussions with interested parties concerning the possible divestment of its 49% shareholding in Virgin Atlantic.” But it adds, “These discussions may or may not result in a transaction.”

The disclosure came after U.K. newspaper The Sunday Times, without citing sources, reported that Delta is in talks with SIA to buy its 49% stake in Virgin Atlantic. The report also says Delta’s SkyTeam partner Air France-KLM is planning to buy part of the Virgin Group’s 51% stake in Virgin Atlantic.

Delta, meanwhile, is not commenting on the story, calling it rumor and speculation.

If Delta proceeds with the acquisition, the move would provide a major boost to SkyTeam’s access at London Heathrow, and at the same time curtail Star Alliance’s reach at the airport, which has been limited by Lufthansa’s sale of its BMI division to International Airlines Group unit British Airways. BA currently is the dominant player on transatlantic services from Heathrow, a position that is strengthened by its joint venture with Oneworld partner American Airlines.

In contrast, Virgin Atlantic’s strategic position has become weaker as its competitors grow. This prompted the airline in 2010 to appoint an adviser to investigate potential growth options, including alliance membership and buying a stake in another airline. Richard Branson, Virgin Atlantic’s controlling shareholder through his Virgin Group, has said that he wants to remain involved in the airline even if part of the carrier is sold.

Virgin Atlantic’s biggest asset is its transatlantic network from London Heathrow, the main gateway into the U.K. and one of the world’s most important business destinations.

But Virgin Atlantic has been losing money. In the 12 months ending Feb. 29, Virgin Atlantic posted a loss of £80 million ($128.3 million), compared to a profit of £18.5 million in the previous year. The airline’s chief executive, Steve Ridgway, at the time said the loss was due to “sky- high fuel prices,” global economic uncertainty and a 25% increase in passenger duty fees. Ridgway is due to retire from his position in early 2013.

Virgin Atlantic is particularly vulnerable to high fuel prices. Its fleet of 42 aircraft includes four Airbus A340-300s, 17 A340-600s and 13 Boeing 747-400s. These four-engine aircraft types burn more fuel and are more expensive to maintain than newer models. The airline has taken steps to update its fleet by ordering 16 Boeing 787-9s and six Airbus A380s. First delivery of the 787-9s and A380s is in 2014 and 2015, respectively, says Virgin Atlantic.

Despite the cost exposure, Virgin Atlantic has valuable airport slots and may be of strategic importance to a U.S. carrier. It will still be difficult for SIA to secure a price comparable to what it paid for its stake in early 2000.

SIA paid £600.25 million for the 49% share, which included a capital injection of £49 million. The deal valued Virgin Atlantic at £1.2 billion, but SIA has since written down the value of the shareholding.