Globo Esporte reports City have tabled a €10m bid to Gremio for the 17 yer-old prospect.
Gremio are on the brink of accepting the proposal, though are yet to sign off on the agreement.
A member of Brazil's U17 World Cup winning team, Rosa turns 18 a week after the European transfer window closes this year. As such, he isn't expected to join City until January.
City have already signed Rosa's Brazil youth teammate Yan Couto from Coritiba this summer.