The company has reportedly appointed investment bank Rothschild and Co to discuss options on a potential sale.
Last month, the company announced its “group transformation plan” where it said it would focus on accelerating growth under Naked Wines, which could include migrating customers, selling assets and closing stores.
Majestic Wine said the details of its decision would be revealed in June as part of its full-year financial results.
At the time, Rowan Gormley, group chief executive, said: “Where we have no choice but to close stores we will aim to minimise job losses by migration into Naked.”
The company employs roughly 1,000 people. A spokesman said more details on the potential sale of its outlets would be provided on 13 June.