Negotiations between City and the Ligue 1 champions are reported to be in progress and Monaco are claimed to be holding out for close to £50 million for the 22-year-old contracted to the club until 2021.
City recently secured the signing of right-back Kyle Walker for £50m, but are reportedly set to improve on that by making Mendy the most expensive defender in history.
The left-back, who joined from Marseille in June 2016, was left out of their recent tour of Switzerland due to an injury he picked up on international duty with France, and further misses out on their pre-season preparations.
The French side face Sporting in Portugal and travel without Mendy and Joao Moutinho, but Real Madrid and Paris Saint-Germain target Kylian Mbappe and Thomas Lemar, subject of a €35m (£30.7m) offer from Arsenal, make the 23-man squad.
Madrid are prepared to make a world record bid for Mbappe after the £70m sale of Alvaro Morata to Chelsea, but Monaco are prepared to offer him a new deal which will make him one of their highest-paid player alongside Radamel Falcao.
This week, Monaco condemned clubs clubs for making approaches to the 18-year-old striker without their permission.