NEW YORK — LVMH Moet Hennessy Louis Vuitton may be slimming down its Selective Distribution Group, after all.

The company is in talks to sell Solstice, the six-unit sunglass chain with headquarters in San Francisco, to the Safilo Group, according to industry sources.

LVMH launched Solstice in 1999 under the group’s umbrella, which also includes the Sephora cosmetics chain. In recent months, speculation has been mounting that LVMH was looking to sell the beauty division, with Germany’s Douglas often touted as a possible buyer, as reported.

While LVMH has denied a desire to sell any divisions, market sources said the deal with Safilo was either imminent or had already taken place.

“I cannot confirm anything,” said Claudio Gottardi, president and chief executive officer of Safilo USA. LVMH did not return calls.

For LVMH, the launch into sunglass retail marked part of its ambition to become a retail specialty force in the U.S. But the slowdown in the economy, particularly after Sept. 11, has hit retailers hard, and many luxury firms, including LVMH, have issued a string of profit warnings.

Solstice operates six U.S. units: at the Garden State Plaza in Paramus, N.J.; Tyson’s Corner in McLean, Va.; Florida Mall in Orlando; South Park Mall in Charlotte, N.C.; the Valley Fair Mall in San Jose, Calif., and at Glendale Galleria in Glendale, Calif.

The chain stands out for its unusual display format, offering designer, bridge, active and sports sunglass lines organized by lifestyle sections and by brand or designer name, and the top 10 sellers from the week before. It also has a computer kiosk system, which has a touch screen that takes the shopper’s picture and then suggests sunglasses, from lines such as Christian Dior, Gucci and Oliver Peoples.

Industry sources said that Solstice, estimated to be worth less than $10 million, was a loss-making business for LVMH, which could be seeking to focus on its larger, high-profile fashion businesses, including Christian Dior, Donna Karan, Celine and Fendi.

One source speculated that the operation was part of a bigger Dior package that also involved the renewal of the license. In mid-December, Christian Dior renewed its license agreement with Safilo Group. In the new agreement, Safilo will dedicate its high-tech production facility in Linz, Austria, to the Dior brand, which accounts for about 10 percent of Safilo’s business. Safilo’s overall sales were projected to reach about $744 million last year.

For Safilo, acquiring Solstice offers an opportunity to help increase the visibility of its luxury brands in an upscale retail environment, while securing its distribution in a competitive retail sector. The Padua, Italy-based company also manufactures licensed lines for design houses such as Gucci and Kate Spade.

The sunglass category is growing into a year-round business, with many status fashion brands aiming for a share of the market. Its retail scene is increasingly controlled by manufacturers owning retail chains, potentially only offering merchandise produced in-house.

Over the past year, sunglass manufacturers have quickly snapped up existing chains. Luxottica Group SpA purchased the industry’s dominant U.S. specialty retailer Sunglass Hut last year in a deal worth about $653 million, including the assumption of the retailer’s debt. Oakley Inc., meanwhile, completed its acquisition of Iacon Inc., a 40-unit sunglass chain operating under the names Sunglass Designs, Occhiali da Sole and Sporting Eyes, with headquarters in Scottsdale, Ariz.