City failed to sign Aston Villa midfielder James Milner and have now turned their attention to Ramires, according to The Mirror.
The £30million-rated midfielder impressed City boss Roberto Mancini at the World Cup this summer.
Real madrid, Chelsea and Fiorentina are also reportedly interested in the 23-year-old.
Ramires joined Benfica from Brazilian side Cruzeiro in a £5million deal last summer.