The Belgian centre-back has become one of the world’s leading defensive talents while at the Citizens, and was a key member of their Premier League winning side of 2011/12.
But, despite his importance at the Etihad Stadium, Monaco are hopeful that they can lure him to France with a financially lucrative deal.
The newly promoted Ligue 1 side are one of the few teams on the planet that can compete with City in terms of cash, thanks to the backing of billionaire Russian owner, Dmitry Rybolovlev.
Despite having spent in excess of £150m over the summer, the principality-based outfit are still keen to spend, and have made a defensive leader their top priority.
Kompany fits the bill perfectly, which could see him become the subject of a serious offer in January.
Monaco are hopeful that the lure of a huge tax free salary and the chance to compete for the Ligue 1 trophy may be enough to convince the 27-year-old to call time on his City career.
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