In a surprise announcement, the Clarets parted ways with Dyche after a spell of nearly a decade, with the team in the relegation zone.
Dyche had already experienced relegation from the top flight while at Turf Moor, but he got the Clarets back to the Premier League at the first attempt.
The former Burnley boss also led the Clarets to the Europa League and their decision to sack him has been the subject of criticism.
Now, in their search for a replacement for Dyche, the Clarets have added current West Brom boss Bruce to the list.
Bruce joins fellow Championship bosses Chris Wilder and Wayne Rooney in being linked with the Burnley job.
Other names being thrown about include Sam Allardyce and Rafael Benitez, but whoever ends up in charge faces the tall task of guiding Burnley to avoid the drop.
Bruce has already been sacked from a Premier League job this season, at Newcastle United, and it remains to be seen if he will be willing to leave West Brom, whom he only joined in February.
