Ancelotti's future at Stamford Bridge has been the subject of speculation with the Blues set to finish the season without a trophy.
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."