The Sun says despite the offer of a three-year contract worth £18million, the 48-year-old Italian spurned Chelsea's advances and decided to stay at Milan on £3.8m a year.
It is a bitter personal blow to billionaire Roman Abramovich, who took on the role himself of finding a replacement for Avram Grant.
The two men had dinner in a restaurant in the Swiss city nine days ago, when Abramovich invited the San Siro chief to offer him some advice.
Ancelotti played with Rijkaard in the legendary AC Milan side, winning two European Cups, while Mancini was a team-mate in the Italian national team.
Both men, he told Abramovich, would make a good choice as coach for Chelsea.