The Daily Express reports that Monaco could make a move for the defender in January.
The Belgian defender was linked with Monaco and Barcelona in the summer, but ended up staying at City.
City are keen to keep Kompany at the club. The 27-year-old’s contract at City is set to expire in 2018.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.