Globoesporte says City's owners City Football Group (CFG) have agreed terms with Gremio for the teenager. City will pay €11m up front with a further €1m due next year. The fee will eventually rise to €23.5m.
Rosa has signed a pre-contract and already announced the agreement on social media.
The youngster is flying to Europe and is expected to train with City before being loaned to Spanish sister club Girona.