Ancelotti's future at Stamford Bridge has been the subject of speculation with the Blues set to finish the season without a trophy and he is expected to be shown the door at the end of the current campaign.
Mancini, whose own future at City had been in question in recent months, with reports in Italy linking him to Juventus, told Studio Sport XXL: "In reality, I have not said no to Juve simply because I have never been approached by them.
"I want to remain at City to build a group. It would be stupid to have to start over somewhere else.
"For the same reason, Abramovich would make a huge mistake to part with Ancelotti. He is one of the best coaches in the world.''
Mancini also spoke about City's Italy striker Mario Balotelli and denied reports of rifts with the 20-year-old.
"He is a good lad,'' Mancini said. "He makes mistakes and needs to grow up. But it's not true that I tell him off. It's just that we speak a lot and one of the things I tell him is that nothing should be taken for granted and that he needs to prove he deserves his place in the team.''