Shakespeare, who was 18/1 with Sky Bet earlier this week, is now 9/1 with the same bookmakers - making him the new second favourite to take the Baggies role.
The 54-year-old dragged Leicester away from relegation danger after his initial appointment late last season, landing him the role on a permanent basis.
Shakespeare played, worked and coached for the Baggies, whom he also managed on a caretaker basis in 2006, before two spells at Leicester and one at Hull.
Both he and another former West Brom employee, Sam Allardyce, whom Shakespeare assisted during his brief spell as England manager, share odds of 9/1 with Sky Bet and are behind only Alan Pardew (1/6) on the bookmakers' list of likely appointments.
Could Shakespeare land the West Bromwich Albion job?