The 36-year-old left the Etihad Stadium at the end of the 2018-19 season to become player-manager at Belgian side Anderlecht, before retiring from his playing days and signing as the permanent boss on a four-year deal in 2020.
Anderlecht have since recorded consecutive third-place finishes in the Jupiler Pro League, where they play their final fixture in the playoff rounds at Club Brugge on Sunday.
Kompany could be set for his first managerial position in the Premier League this summer though, with Manchester Evening News reporting that the Belgian is the leading candidate to take over at Burnley ahead of the 2022-23 campaign.
However, the report outlines how any potential deal supposedly hinges on which division the Clarets will compete in next season, as they look to retain their top-flight status on the final day at home to Newcastle United on Sunday.
Mike Jackson has overseen a successful caretaker period since stepping in to cover for the sacked Sean Dyche back in April, with an impressive return of 10 points from his opening four games seeing him pick up the Premier League manager of the month award.
Burnley earned a 1-1 draw at Aston Villa on Thursday evening to lift themselves out of the bottom three ahead of the final day, with goal difference keeping them above Leeds United, who travel to Brentford in their final game.