Cole had a 20-minute heart-to-heart with Ancelotti at Chelsea's training ground after reporting back last week.
And the 29-year-old England full-back stressed he feels he needs to leave the club now and move abroad to link up with former boss Jose Mourinho in the wake of his marriage break-up with pop star wife Cheryl and lurid stories about his personal life.
A source close to Chelsea told Sport 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.
Spanish giants Real have been monitoring Cole's situation closely and are now poised to launch a £25million bid.
It is understood Real and former Chelsea boss Mourinho has been very supportive of Cole following Cheryl's divorce announcement, although there is no suggestion he has made any formal overtures to the player.
Ancelotti is believed to have been sympathetic to Cole's position, but does not want him to leave. Our 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."
Cole has been criticised for not visiting Cheryl, who is currently recovering from malaria, and has reportedly been very solemn in training.
Cole is due to play for Chelsea in tonight's friendly against Frankfurt in Germany.
Cole's agent David Manasseh said: "I have no comment to make."
The Cole situation could be a first test for Txiki Begiristain, the former Barcelona football director Chelsea hope to bring to Stamford Bridge this month.
Marked man: Ashley Cole, in pre-season action for Chelsea against Eintracht Frankfurt
ASHLEY COLE was last night told to forget any idea of quitting Chelsea. Carlo Ancelotti has told Jose Mourinho to forget about sweet talking Ashley Cole to Real Madrid.
The Real boss is banking on the relationship he forged with Cole during his time at Chelsea as his trump card when it comes to landing the England left back.
But Ancelotti hit back insisting the only professional relationship that counts for anything is the one he has forged with the 29-year-old.
Cole, 29, has been under fire since his split with pop star wife Cheryl Tweedy last year following revelations of sordid text sex with other women.
Now Cole, who signed a £100,000-a-week deal to 2013 last summer, is hoping ex-Blues boss Mourinho will make a £20million move for him.
'I'm not interested in the relationship my player has with other coaches,' said Ancelotti. 'It's normal that Mourinho has a good relationship with Ashley Cole.
'Nothing has changed in our position. He is a Chelsea player and will remain a Chelsea player for the future. There's no way he will leave. Everyone can forget that Ashley Cole will leave this club.'
The break-up of Cole's marriage to pop-star wife Cheryl combined with recent comments about hating England and the English mean Real are ready to offer him a way out by lodging a £20million bid.
But Ancelotti is adamant no offer will prise Cole away, insisting: 'There is no price, there is no price. We believe he's the best left back in the world and because of this he will stay at this club.'