Sources have told ESPN the teenage forward will move to City for €10m plus add-ons and is likely to be loaned out next season.
City confirmed the news in a statement.
“We are delighted to confirm we have reached an agreement with Fluminense regarding the future transfer of Kayky,” it read. “The teenage forward will remain with Fluminese until the end of the Brazilian season.”
This season the 17-year-old has scored two goals in eight appearances for Fluminense.