The Manchester City legend is in his third season in charge at the Belgian giants.
And his work, reports the Telegraph, has brought Kompany to the attention of Burnley's owners, ALK.
The Clarets are seeking a new manager after the sacking of Sean Dyche earlier this month and Kompany is being considered.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!