The Clarets are on the hunt for a new manager to take over at the club, having parted ways with Sean Dyche in April.
Burnley handed Mike Jackson the temporary reins to try to keep them afloat in the Premier League, but a 2-1 loss to Newcastle United on the final day of the season saw them slip down to the Championship.
Anderlecht coach Kompany and former Braga coach Carlos Carvalhal are among Burnley’s shortlist of managerial candidates, with the Belgian emerging as the favourite.
It had been claimed that Kompany would only move to Burnley if they had managed to stay in the top flight, which they have failed to do.
However, the Lancashire outfit are yet to give up on their hopes of appointing Kompany and are waiting to hear what his decision is.
Burney may only move to another candidate if they receive a clear indication from Kompany that he is not interested in the job.
It remains to be seen who Burnley will appoint as their next boss, as they prepare to deal with the financial implications of losing their top flight status.
