It’s understood that the 22-year-old has emerged as a top target for the reigning Premier League champions, and that the player himself travelled to England last week to discuss a January move to the Etihad Stadium.
The trip is said to have taken place on Tuesday, but the starlet himself did not attend City’s Champions League win over Bayern Munich in a bid to keep the potential switch secret.
United and Chelsea have also been linked with Kurzawa, who is seen as one of French football’s top emerging full-backs.
Although Monaco are far from short of cash, the Mediterranean outfit are believed to be aware that they may be unable to hold onto their man, making offers of around £17m tempting.
City are eager to win the race as they step up their New Year plans, which also include extending Frank Lampard’s loan spell from New York City FC.