The 21-year-old has been with City since arriving from Fluminense in April 2021.
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He did feature in the Premier League and the FA Cup in 2021-2022, but has not since played for their first team.
Now he is heading to Dutch top-flight club Sparta Rotterdam on a season-long loan deal.
Kayky has spent time at Portuguese club Pacos de Ferreira and Bahia in Brazil.