The discount booze retailer was placed into administration several days ago amid reports that its owner Conviviality had been hit by a £30 million tax bill.
Conviviality, which has about 20 Bargain Booze and Wine Rack stores across South Yorkshire, said in a statement: "The sale secures continued employment for circa. 2, 300 employees of the Conviviality retail business and provides continuity of trade for suppliers and franchisees."
Paul Taylor, area organiser, said: "Clearly this is a very worrying time for our members, with all the uncertainty that goes with the sale of a business.
"We are working with the company to ensure that the staff are protected through the sale process and we’ll be seeking an early meeting with any new owner. In the meantime, Usdaw is providing our members with the support and advice they require.”