The 23-year-old has emerged as a top target for new City boss Enzo Maresca, per Football 365.
Gusto has worked under Maresca previously at Stamford Bridge, and the deal could move quickly given their strong relationship.
But City have their work cut out if they want to land the Frenchman, as The Blues are demanding a hefty £75 million for Gusto's signature.
It is believed that if that figure does not drop, City will be forced to look at other options elsewhere as they look to strengthen their defence ahead of next season.
And with Marc Cucurella having already departed for Real Madrid, Chelsea will undoubtedly be reluctant to let another one of their top full-backs go this summer.
