The 29-year-old is keen to leave Chelsea and link up with former boss Jose Mourinho at Real Madrid.
A source close to Chelsea told News of the World: “It was a very amicable meeting, but Ashley made it clear that because of his personal situation he feels it is in his best interests to leave the club.
“He told Ancelotti that he will be very sad to leave and that it had been a privilege playing for the club during such a successful time in its history.”
Real Madrid are reportedly ready to make a £25million bid for Cole.
News of the World’s source added: “Ashley was told that he would have to go and see the chairman, which he hasn’t done yet and he has not handed in a formal transfer request.
“He knows Ancelotti wants him to stay, but he feels that moving abroad is the only way he can escape the attention after what happened with Cheryl and the other stories about his private life.”
