The Serb enters the final year of his contract this summer and is the subject of interest from Napoli, Juventus and Galatasaray, where Mancini remains an admirer.
City is understood to be planning to discuss an extension in the coming months, however, with Kolarov significantly happier with his role at the Etihad Stadium this season.
"Last season I was thinking, because I didn't play a lot, that maybe it was a good thing for me to move," he told the club's official website.
"I had a couple of opportunities, but in the end I refused everything because I didn't want to go from here. I hadn't shown the people what I can do. Now, this season, I think I have shown what I can do. For me it has been a victory, personally, for myself."
Kolarov has been rotated and sometimes been used in tandem with rival Gael Clichy on the left flank by Manuel Pellegrini, but feels he has been treated fairly by the Chilean.
"We know that at this level you always have another player who is playing in your position. Until now the boss has rotated the team and I think we have done well.
"Of course me and him want to play every game, but the boss makes his choice and we are professionals.
"Maybe if someone is not happy then at the end of the season you can talk and you can find a solution, but both of us have played a lot so now it is important for us to win the trophies."