The 27-year-old was linked with a move away from the Premier League outfit in the transfer window, with Juventus reported to be among his suitors.
But he has now underlined his commitment to Manuel Pellegrini's side.
"There were a lot of things said in the papers, but I never said I wanted to go," he said.
"I have two more years of contract at City, so I'm focused on working hard in training and, when I have the chance to play, giving my best. I am happy at City and one or two years - we'll see what happens."
The Serbia international - who started City's last game before the international break against Hull City - feels that Pellegrini can help push the club on after a disappointing campaign last time round saw them relinquish their title.
"He did very good things with Villarreal, and with Malaga last season, so I think has a lot of experience, which is good for us," he added.
"The first game against Viktoria Plzen is a big one for us, because a lot depends on how we start the Champions League. It’s important for us. We want to improve in the Champions League after two not-very-good seasons in it."
Kolarov scored in Serbia's 3-0 win over Wales on Tuesday night in a FIFA World Cup qualifying match.
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