The England international has lost his place in the starting lineup to young Serbian centre-back Matija Nastasic this season, which has resulted in reports that he is surplus to requirements at the Etihad Stadium.
However, despite his lack of appearances, 30-year-old Lescott has expressed his eagerness to stay put.
"I'd love to stay here but if it is not to be, then so be it. The manager has said nothing, just that I should continue to give 100% effort," the Manchester Evening News quotes him as saying. "It has not been the greatest of seasons in terms of appearances but I'd like to think that when I have played I have given 100% effort.
"I would definitely like to stay with the way the club is progressing – we have an opportunity to win another trophy this year, so we could be one of the few clubs in England to win something.
"It is a special club to me now. I've been here a long time and they showed a lot of persistence to get me here. I feel like we've done a lot together. I'm older now and I'm not naive enough to think I'm definitely going to stay, but if I do then great."
Lescott joined City from fellow Premier League side Everton in 2009.