Bruce managed to oversee only one win from 13 league games in the Championship during his time at the club.
West Brom are winless since the fifth matchday when they beat Hull City 5-2, with that run including five draws and three losses.
With the Baggies currently in the relegation zone, the axe fell and Bruce was relieved of his duties, with current Under-21s manager Richard Beale taking over in the interim.
Keane has now emerged as the early favourite to replace Bruce, with that possibility gaining traction after the former Republic of Ireland midfielder was seen in the stands during the Baggies’ loss at Preston North End.
The 51-year-old is currently without a club after having last served as assistant manager of Nottingham Forest towards the end of the 2018/19 season.
West Brom travel to fifth-placed Reading on Saturday, with the Royals dropping points at home to only Norwich City and Sunderland.
The Baggies have just eleven points from 13 games, with their record being one win, eight draws and four losses so far this season.
