The Manchester City legend is in the second year of a four-year deal with the Brussels club, who he has taken to third-and fourth-place finishes in the First Division A after leaving the Etihad.
However, it has been suggested that the former Belgium international is top of Alan Pace’s wishlist to replace Sean Dyche, as a modern coach with an attractive reputation, who is prepared to work with data in terms of player acquisition.
Kompany’s family home remains in Manchester, and, as at Anderlecht this summer, whwre a rebuild is expected at Lotto Park, he would face a situation at Turf Moor where nine players are out of contract, two of which – Ashley Barnes and Jack Cork – have options in the club’s favour.
HLN reported this morning: “It's not that Kompany and Anderlecht are tired of each other, the fans hold him in high regard.
"The question is whether Kompany is prepared to start all over again in the Lotto Park.
"This summer a lot of strong players will probably leave Neerpede again and a number of newcomers will therefore have to be fitted in.
"With a third and fourth place, Kompany led Anderlecht again towards the second top.
"But how much progression margin is there in the current context at Anderlecht?
"This question undoubtedly haunts the mind of the ambitious Vincent Kompany. The answer may send him again across the Channel.”
Kompany spoke on the speculation last month, saying: “Finally some rumours.
"That's the first time. Actually, I just don't respond to it. I am so focused and driven by what needs to be done on Sunday. Especially after Union, I don't pretend to be the coach that is in the interest of many clubs. I just want to win on Sunday. I just want to say: I've been a coach for two years now. Of course it happens that people sometimes inquire or call me. I'm a very private person, so usually there are never rumors around me. But if that ever happens, then so be it.”
He added: “In this industry names are mentioned. Coincidentally, last week I was in England for the award (he was inducted into the Premier League Hall of Fame).
"Maybe then people had the idea to start betting on me en masse. It's just normal for there to be interest left or right, but how I deal with it is to: a) not concern myself with it. And b) focus on Anderlecht.”