The Serbia left-back joined City from Serie A side Lazio in 2010 in an £18 million transfer deal and helped the club to the Premier League title this season.
However, Mancini has insisted Kolarov remains part of his plans.
"Kolarov? He is a great left-back and I would like to keep him," Mancini told Italian TV station Sky Sport 24. "We have very good players and there many clubs interested in them, which means that we have done our jobs well. We know his (Kolarov's) value well and we want to keep him."
Kolarov, who made just 12 league starts for City this season but was often preferred to Clichy in the Champions League, is under contract until June 2015.
Meanwhile, City have announced that Piaggio Aero Industries chief executive Alberto Galassi has joined their board of directors.
Galassi was previously on the executive committee of the aircraft manufacturing company, where he was responsible for marketing and sales and has been a member of the bar since 1996, specialising in international commerce and arbitration.