The City skipper is preparing to lead Belgium out at the World Cup after celebrating Pep Guardiola's squad recently strolling to the Premier League title.
Kompany has spent a decade at the Etihad and is in the final year of his contract, with chairman Khaldoon Al Mubarak insisting earlier this week the 32-year-old talisman could have a job for life with the club if he wants it.
His Manchester-born wife, Carla, however, a life-long City fan, told radio station XS Manchester's Forever Blue show: "That would be the cherry on the top of the cake wouldn't it, if he became a (City) manager in the future - I would absolutely love that.
"He has definitely got the ability to get there. But I'm not sure if that's something he will go into. He has done his MBA, he's a businessman as well and is very intelligent.
"There are lots of things he could do once his career playing football is finished. The world's his oyster, really. He could be prime minister, he could be anything!"
Kompany is already guaranteed legendary status at City but Guardiola still retains a concern over the central defender's ability to stay injury free, having been plagued by problems in recent seasons.
The Belgian still believes he has a couple more years left in his legs, although a future position in the club's wider City Football Group of clubs would likely be forthcoming.