The Serbian international, who joined from Lazio in 2010, only started 11 Premier League games last season and was namely used when regular left-back Gael Clichy was unavailable.
Kolarov's role under new manager Manuel Pellegrini has not be specified and the defender did not rule out a move to the Serie A Champions.
"I'm happy at City and it is my intention to remain," the 27-year-old told Tuttosport.
Turkish side Galatasaray had a £4m bid for Kolarov rejected last week, with City holding out for at least £5m to seal his exit from the club.
Juventus to date have only offered a loan deal where they would take on the defender's £100k-a-week wages on in full.
The Italians have already raided City once this summer for the signature of striker Carlos Tevez who arrived in a deal worth up to £10m.
City have been busy in the transfer market this summer spending over £90m on Fernandinho, Jesus Navas, Alvaro Negredo and Stevan Jovetic.
The club are keen to offload a number of players such as Kolarov as they seek to pursue their interest in Real Madrid defender Pepe.
Manager Manuel Pellegrini is hopeful he can complete a £20m deal for the Portuguese international before the close of the summer transfer window on September 3.