The 27-year-old Serbia international was strongly linked with a move away from City during the summer transfer window, with Juventus credited with an interest in the full-back.
However, Kolarov insists he has no plans to quit City and is focused on fighting for his place in Manuel Pellegrini's side.
"There were a lot of talk about Juventus but I never said I wanted to go," Kolarov told The Sun.
"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 so now we'll see what happens. I am professional and I will be looking to win something this year."
City kick-off their UEFA Champions League campaign next week against Viktoria Plzen and Kolarov admits they are looking to make an impact in Europe this term after crashing out at the group stages in the last two seasons.
"That competition is important for us," added Kolarov. "Last year was not good but now we've a good group and we can go through.
"Pellegrini did very well in the Champions League at Villarreal and Malaga. He has experience and that will be good for us."
Manchester City Fixtures .
Saturday September 1415:00 Stoke City v Manchester City
Sunday September 2216:00 Manchester City v Man Utd
Saturday September 2815:00 Aston Villa v Manchester City
Source: Manchester City MAD