Lescott has established himself as a key figure at the Etihad Stadium since his arrival from Everton and remains under contract until the summer of 2014. The England international defender is keen to commit to the club for even longer but recognises that he must keep performing to a high level if he is to earn an extension.
"I've got this season and one more. I'd love to extend it and finish my career here," said the 30-year-old.
"Going knocking on doors isn't my style. I don't think my mum would be happy if I did that. I just continue to be professional.
"I know where I've come from. A few years ago I was playing away at Plymouth on Tuesday nights. Now Tuesday evenings mean Champions League.
"I'm grateful for what I have now. So I won't rock the boat."
Lescott has accepted that he will not play every game because City's squad is so strong, although he admits it was disappointing to be rested for the Champions League clash with Real Madrid last week.
"Obviously it hurt but the manager picked the team and I wasn't in it," said Lescott, who returned to the starting line-up against Arsenal and scored in a 1-1 draw.
"It's a great stadium, a great occasion for the club and you want to pit yourself against the world's best, like Cristiano Ronaldo.
"But I just have to work hard. It's happened before over the last couple of seasons.
"I've played, been left out. It's happened before during my career and I'm ready for the fight."