Leslie Wexner, the billionaire behind Victoria’s Secret, is in discussions to step aside as chief executive officer of his retail empire and is exploring strategic alternatives for the lingerie brand, according to people familiar with the matter.

The parent company, L Brands Inc., is in discussions with Sycamore Partners, a private-equity firm that has scooped up several troubled apparel brands, some of the people said. The discussions are ongoing and could result in a full or partial sale of Victoria’s Secret, some of the people said.

The chain, with about $7 billion in annual sales, has long dominated the U.S. lingerie market but has struggled in recent years with falling sales. The company is looking to reach a decision on the potential deal and succession plans in coming weeks, some of the people said.

Mr. Wexner, 82 years old, who built Abercrombie & Fitch, The Limited and Victoria’s Secret into national chains, is the longest-serving CEO of an S&P 500 company. He would be handing over the job after a difficult stretch for the business he has run for 57 years. He could continue in his role as chairman, one of the people said.

Shares of L Brands Inc. dropped 29% last year, missing out on a broad stock market rally. The company, which also owns the Bath & Body Works and Pink chains, has a market value below $6 billion, down from $29 billion at its peak in 2015. The shares soared 13% Wednesday after The Wall Street Journal first reported on the possible moves.