Pulis was dismissed by the Baggies earlier in the week just a couple of days after they were soundly beaten by Chelsea to extend their winless run - which began all the way back in August.
The Star reports that Alan Pardew is the favourite for the post, while Sam Allardyce has also been linked with being a possible contender given his reputation for getting teams out of trouble and his previous links to the club.
However, it appears that one Premier League boss is also being considered for the post - though it is not clear how serious the Baggies' interest is or whether the manager in question is at all interested in considering the job.
Dyche has received a huge amount of plaudits this season for the work that he has done at Turf Moor, guiding Burnley to seventh in the table this term after keeping them up last year.
Should they beat Arsenal on Sunday, Burnley will go fourth in the Premier League just three points adrift of second place Manchester United. And while few are expecting the Clarets to still be in those positions come the end of the season, Dyche's men look more than set to potentially secure a third consecutive season in the top flight - which would be the first time Burnley have done that since the 1970s - so it is no surprise that West Brom are considering him.