However, Carlo Ancelotti - along with assistant Ray Wilkins and chairman Bruce Buck - has repeatedly said Cole will not be sold at any price and Mourinho has accepted Chelsea's stance.
"Carlo Ancelotti was very, very clear and that's the best way in football," he told the Sunday Times. "He killed the story by saying, 'No money can buy Ashley Cole, Ashley Cole needs to stay'.
"I think Ashley thought about leaving for personal and professional reasons. We thought about him because he's a good player who I enjoyed working with, but when a coach says no, it's no, and we have to accept that."
The Real coach has also suggested that he is unlikely to offer for his former player Ricardo Carvalho, as the defender, who has expressed a desire to leave Chelsea, is too old.
"Ricardo is also a good player, but he is at an age that, if somebody is looking to build a team for the future, he cannot think of him,'' Mourinho said. "Ricardo belongs to the current moment. He is a man with a great professional and private life, so he has no problem when it comes to playing at a high level at the age of 32.''
Mourinho has also acknowledged that Real have no chance of signing Liverpool captain Steven Gerrard, who has in any case committed his future to the Reds.
"He is part of the history of Liverpool, he belongs to the club - he is too important to them,'' Mourinho told reporters in Los Angeles. "The same thing happened when I tried to take Frank Lampard to Inter Milan.
"The problem exists when a club buys a player that is 30 and that cannot be sold later on.''