All the Big W sites have A1 consent, meaning they can sell anything from home goods and clothing, some of the stores will also be able to sell food.
And Wal-Mart is believed to be first in line for the stores as it looks for space for its standalone George clothing shops.
Following the success of the George range in Asda stores, the first George stores opened in Leeds and Croydon in September. Two more are planned for May, in Preston and Northampton.
Woolworths and property agent Colliers CRE have drawn up a list of prospective tenants, with Wal-Mart at the top, along with other possibles such as Marks and Spencer, Next, Currys and Comet, TK Maxx and Matalan.