Kompany is on a shortlist of candidates to succeed Sean Dyche at Turf Moor and no decision has been made yet over their next manager.
Burnley have been without a permanent boss since sacking Dyche in April and though caretaker manager Mike Jackson picked up 11 points from eight games in charge, he was not able to save the Clarets from relegation to the Championship on the final day of the season.
Kompany confirmed his departure from Anderlecht on Wednesday, with a club statement reading: “Today only one feeling prevails: I am proud that I was able to start this new chapter at the club of my heart. I have now been a player and a coach of RSC Anderlecht, but above all I remain a loyal fan.”
Kompany was first named player-manager of Anderlecht after leaving the Etihad in 2019, but after presiding over their worst start to a league season, he returned to playing duties for the rest of the season.
In August 2020 he was given the role again on the same day he announced his retirement from playing. In his first season, he led them to fourth in the Belgian first division. This campaign he went one better, with the club finishing third.
Ahead of their final game of the season with Club Brugge on Sunday, Kompany had cast doubt over his future, telling reporters: “I will sit down with the board [this summer]. We’ll see if the goals for next season are achievable. Shouting about winning is one thing, doing it is another.”
There had been reports of friction between the manager and the Anderlecht hierarchy after owner Marc Coucke posted on Instagram in April ‘How to kill an entire season in 1 week’ following a poor start to the play-offs, and defeat in the Belgian Cup final to Gent.
As a player, Kompany spent 11 years at the Etihad, making 360 appearances and scoring 20 goals – including a potentially title-winning strike against Leicester City in 2019, which helped the club lift the last of the four Premier League titles they earned during his stay.