The Italian was in charge when City won the Premier League title in 2011/12, their first since 1967/68. But he struggled in Europe's premier competition with City, having only ever reached the last-16.
With Pep Guardiola now in charge, the Sky Blues have mustered an almost insurmountable lead at the top of the league, and yesterday, they beat Basel 4-0 in the first leg of their Champions League last-tie.
Asked if City could win it all, Mancini said: "Maybe they can. Manchester City improved a lot this year.
"Now the level is very high and they could have a chance to win the Champions League."