Wise, who has odds of 5/2, only misses out on being the favourite due to Keith Hill's slim odds of 5/6, is now believed to be among the favourites to replace Dean Keates with Walsall FC expected to name their man in the days after next weekend's season-ending clash with Shrewsbury Town.
The Saddlers go into the match on the back of last weekend's welcome win over Peterborough United with a slim chance of retaining their place in League One for at least another season as a win and a couple of favourable results elsewhere could see them rise out of the dropzone and back into safety.
Wise, a former England international who also counts Leicester City, Southampton, and Coventry City among his former clubs, has limited managerial experience having undertaken caretaker spells at Millwall and Southampton along with short-term stays with Swindon Town and Leeds United.
Walsall FC are unlikely to respond to any of the latest round rumours as they look to secure a spot in the third tier of the game for at least another season.