Sources have told ESPN the 17-year-old forward will move to City for €10m plus add-ons.
Man City said in a statement: "We are delighted to confirm we have reached an agreement with Fluminense regarding the future transfer of Kayky.
"The teenage forward will remain with Fluminese until the end of the Brazilian season."
According to Fluminense, City have purchased 80% of the player's rights, with the Brazilian side maintaining 20%.
Kayky has scored two goals in nine appearances for Fluminense so far this season.