The 32-year-old's current contract at the Etihad Stadium expires at the end of the season, and he has so far not been offered an extension to his 11-year stay at the club.
Kompany has fallen down the pecking order for the Premier League champions this season, starting just two league games during City's unbeaten start to the campaign.
A number of top European clubs are understood to be monitoring his situation, and Inter Live reports that Inter have made the first move for his signature.
The Belgian is thought to be at the top of the Serie A outfit's wishlist for next summer, although they are also considering moves for Kompany's compatriots Toby Alderweireld and Jan Vertonghen, as well as his City teammate Eliaquim Mangala.
All four players could be available on free transfers at the end of this season and are seen as possible replacements for Milan Skriniar, who has been linked with Manchester United.