When Sir Richard Branson sold a 49% stake in Virgin Atlantic Airways to Singapore Airlines Ltd. in 1999, the U.K. billionaire described the tie-up as a "marriage made in heaven," with hopes that the alliance would offer customers a much-wider choice of destinations.

But the relationship never quite blossomed the way both partners had envisaged, and now looks set to end after 13 years. On Monday, Singapore Airlines said it was in talks to sell its investment in Virgin Atlantic, a move that if successful would free the premium Asian carrier from one of its most underperforming strategic investments. Mr. Branson's Virgin Group owns 51% of the London-based airline.

"It was pretty clear for a long time that the partnership didn't go deep enough," said Timothy Bacchus, head of transportation research at CCB International Securities.

People familiar with the situation said Sunday that U.S.-based Delta Air Lines Inc. has approached the Singapore flag carrier to discuss buying its Virgin Atlantic stake, though they said there was no certainty the talks would succeed.

Singapore Airlines confirmed in its statement that it was in discussions with "interested parties' on a possible sale, but noted the talks "may or may not result in a transaction." The airline said Monday it had no further comment beyond the statement. Its shares ended flat at S$10.71 ($8.77), tracking the broad market.

Singapore Airlines, frustrated over its lack of involvement in Virgin Atlantic despite their equity links, has been considering the sale of the stake for several years and has held talks with airlines, according to analysts and industry executives. However, they said interest was muted because of a weak aviation market since the global financial crisis.

With its initial investment in Virgin Atlantic having long been written down, cash from the sale could help Singapore Airlines fund an aggressive fleet expansion. In October, the airline ordered 25 new Airbus aircraft, worth $7.5 billion at list prices. It also has 20 Boeing 787 Dreamliners on order for its new budget carrier unit, Scoot.

"This is definitely good news for Singapore Airlines," said Kelvin Lau, a Hong Kong-based analyst at Daiwa Research. The investment "didn't really deliver what the airline was looking for and hasn't really been financially performing."

Singapore Airlines paid 600.3 million British pounds ($962 million) for the stake in Virgin Atlantic and was criticized at the time by financial analysts for having offered too much for a share in the privately held airline. Since then, the cooperation between the two carriers has been largely limited to code-sharing and reciprocal recognition of frequent-flier miles--arrangements that Singapore Airlines also has with nearly 20 other airlines. Virgin Atlantic also doesn't fly to Singapore.

Though it is unclear what prevented further cooperation between Singapore Airlines and Virgin Atlantic, some analysts said divergent markets could be partly to blame: Virgin Atlantic was big in the trans-Atlantic business, while Singapore Airlines was strong on long-haul and regional flights from its home city.

With the investment, Singapore Airlines had sought rights to fly on the key London-New York route. Those hopes, however, never materialized.

Virgin Atlantic has also produced dismal financial results: though it posted operating losses for only two of the last five financial years, the total losses far exceeded the profits made.

Analysts therefore expect Virgin Atlantic to be worth much less than what it was valued at the time of the Singapore Airlines investment, though specific estimates are difficult to formulate because the unlisted U.K. carrier doesn't release detailed financial statements.

Singapore Airlines hasn't been immune to the downturn in first- and business-class passenger traffic and sky-high fuel prices, and last month it reported a 54% slump in net profit for the quarter ended September. It plans to withdraw nonstop flights to Los Angeles and Newark, N.J., at the end of next year because of high operating costs, marking the end of the world's two longest-distance commercial flights. Meanwhile, competition with thriving low-cost carriers is also putting pressure on ticket prices on short, regional flights.

The relationship between Singapore Airlines and Virgin Group has also at times been rocky. In its 1999 investment in Virgin Atlantic, Singapore Airlines acquired the veto rights to use the Virgin brand on other international airlines. Without the Singapore company's consent, Mr. Branson had been unable to use the Virgin brand on new international ventures operating out of Australia.

The ice finally broke last year, when Virgin Australia Holdings Ltd., in which Virgin Group owns a 26% stake, entered a wide-ranging alliance with Singapore Airlines involving coordinated schedules, code-sharing and marketing ties. Virgin's international ventures were also folded into the Virgin Australia brand for the first time. In October, Singapore Airlines bought a 10% stake in Virgin Australia.

--Gaurav Raghuvanshi in Singapore contributed to this article.

Write to Jeffrey Ng at Jeffrey.Ng@wsj.com

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