Last weekend, the Clarets were relegated from the Premier League, a development which will see Mike Jackson depart his role as interim boss.
The club's American hierarchy will instead bring in an outside name as the permanent successor to Sean Dyche, and it appears that a top-flight legend will be returning to English football.
According to transfer expert Fabrizio Romano, the Belgian is close to becoming the new Burnley head coach with talks having already been held between the relevant parties.
The report emerged before the 36-year-old had left his position at Anderlecht, ending a two-year spell with his boyhood club.
Should an appointment be made, Kompany would be returning to the North-West of England having spent over a decade of his playing days at Premier League giants Manchester City.