Cole, 29, has been linked in media reports with a reunion with former Blues coach Jose Mourinho at Real Madrid.
"Ashley Cole will not be sold at any price," Italian Ancelotti told reporters after Chelsea lost 2-1 to Bundesliga club Eintracht Frankfurt in a pre-season friendly.
"There is no price that we would sell him at. We believe he is the best left-back in the world and because of this he will stay at this club.
"Nothing has changed in our position. Everyone can forget about Ashley Cole leaving this club," he added.
Eintracht took the lead through Patrick Ochs and, after England midfielder Frank Lampard had equalised for Chelsea, Halil Altintop struck the winner from the penalty spot.
Chelsea play Manchester United in the Charity Shield, English football's annual curtain-raiser, next Sunday at Wembley.