Exeter City have informed West Brom they want to keep hold of their loan duo.
Both of their loan deals expire this week, but Wilson scored his first senior goal for the Grecians at the weekend and talks are underway to extend the loans until May.
However, neither Wilson nor Edwards will be available for Exeter in their FA Cup third round clash with the Baggies this coming Saturday.
Meanwhile, Tyler Roberts, who has scored five goals for Walsall this season, is on loan at the League One club until January 27, but a number of clubs are circling the 18-year-old, whose contract runs out in the summer.
Albion have already rejected a multi million bid for the teenager, and have offered him a new deal.