The Serie A giants are eyeing the Serbia star, 27, who has fallen behind Gael Clichy in the pecking order at the Etihad.
Kolarov, who joined City for £16m from Lazio in 2010, is keen to leave in search of regular football.
But City want to keep him on board under new boss Manuel Pellegrini.Meanwhile, the Blues are close to a £24m deal for Fiorentina hitman Stevan Jovetic and also want Sevilla striker Alvaro Negredo.
They have already spent big to snap up Brazilian midfielder Fernandinho and winger Jesus Navas for a total of £45m.“ City want to keep him on board under new boss Manuel Pellegrini”
And with Maicon in Italy yesterday finalising a £4m switch to Roma, they have knocked £37m off their wage bill this summer.
City face AmaZulu in Durban on Thursday as their pre-season trip to South Africa continues.