The Clarets decided to part ways Sean Dyche in mid-April following a lengthy spell at the club, as they slipped down to the drop zone in the league.
Burnley Under-23s boss Mike Jackson has been given the temporary reins at Turf Moor but the club are on the hunt for a permanent manager.
Manchester City legend Kompany, who is currently managing Belgian side Anderlecht, is one of the names on Burnley’s shortlist of candidates.
However, the Lancashire outfit are likely to face significant competition for Kompany’s signature as Bundesliga outfit Wolfsburg are also keen on him.
Die Wolfe are looking for a replacement for Florian Kohfeldt in the dugout and have been impressed with the work Kompany has done in Belgium.
The Germans are keen to hold talks with Kompany and could offer him chance to manage in the Bundesliga, while Burnley’s future in the Premier League remains up in the air.
It remains to be seen whether the Clarets manage to maintain their top flight status as that will be key to who they appoint as their new boss.
