The Serbia left-back joined City from Serie A side Lazio in 2010 in an ?18million transfer deal and helped the club to the Barclays Premier League title this season. However, he played second fiddle to Gael Clichy for large parts of the campaign, sparking speculation about his future as Inter Milan and Juventus were linked with a move for the 26-year-old.
However, Mancini has insisted Kolarov remains part of his plans and he told Italian TV station Sky Sport 24: "Kolarov? He is a great left-back and I would like to keep him."
He added: "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.