Reports have suggested Real Madrid boss Jose Mourinho, who was close to Cole during his time at Stamford Bridge, is keen once again to link up with the 29-year-old and is set to launch a big-money bid.
But Ancelotti said: "I'm not interested in the relationship my player has with other coaches.
"Everyone can forget the idea he will leave this club.
"There is no way that will happen. We believe he is the best left-back in the world and because of that he'll stay. There is no price that will make us sell."