Kompany, 27, joined the North West side in 2008 from Bundesliga club Hamburg and went on to play an important role in the squad that captured the Premier League title in 2011/12.
Per Perrin's report, Monaco could make a move as soon as January:
Manchester City skipper Vincent Kompany has piqued the interest of Monaco, who could make a move for him in January.
The towering Belgian defender was linked with the free-spending Ligue 1 giants and Barcelona in the summer - but neither side were able to firm up their interest.
Kompany missed the Chelsea game with a calf injury that he has been struggling to shake off. But Monaco are undeterred and will go on the offensive to prise Kompany away from the Etihad.
Monaco lay joint top of Ligue 1 at present, with Eric Abidal and Ricardo Carvalho featuring as the side's regular central defensive partnership.
However, with a combined 69 years between them, the pair are far from an ideal long-term solution for Claudio Ranieri's wealthy outfit.
Nicolas Isimat-Mirin joined the club from Valenciennes this summer, but the 21-year-old has thus far not been trusted with a minute of Ligue 1 action—despite excelling for his former side last season.
It is clear that Monaco will be in the market for a centre-back in the near future, and judging by the club's ambitions, it will be a big-name signing that arrives.
Kompany, a French-speaker, fits the bill well in terms of profile and ability, as well as bringing important leadership qualities to any side in which he plays.
However, given his importance to Manchester City and his current contract until 2018, it would require a significant investment to bring the Belgian to the principality.
Even by Monaco's free-spending standards, cash-rich Manchester City's demands could potentially rule out a move for the player.
Monaco do, though, need a defender, and it would be no surprise to see them at least make an attempt for a player of Kompany's stature were there to be a suggestion of availability.