The Blues were linked with a £60m summer move for the Portuguese winger along with former club Manchester United and mega-rich Paris Saint-Germain.
But Mourinho, who began his second spell at Stamford Bridge on Monday, revealed that the pair fell out towards the end of his turbulent three-year reign at the Bernabeu because the the player 'thought he knew it all'.
Fall out: Jose Mourinho and Cristiano Ronaldo in the tunnel before Real Madrid's match against Osasuna on Saturday
Final act: Mourinho endured turbulent end to three-year reign at Madrid
Mourinho told Spain Intereconomia: 'He (Ronaldo) had three great seasons with me, I don’t know if they were the best in his career because at Manchester United he had great seasons too.
'But I think we found for him a tactical situation that helped him express himself on the pitch perfectly as shown by goal figures. The only problem has been that a coach criticises him from a tactical point of view trying to improve him and he has not accepted it well thinking, perhaps, that he knows it all and that the coach could not help him become any better.
Leaving Madrid: Cristiano Ronaldo says that he will not renew his contract past 2015
Keeping everything open: Ronaldo may be open to a move back to old club Manchester United
'But there is no other problem. The last two games, which have been the only games in which he has not played because he always played before and he always gave everything for the team, in these last couple of weeks he has had this pain in his back and I don’t ever doubt the players when they say they are injured.'
Mourinho was also asked if Ronaldo’s closest pal at Madrid, Pepe, had betrayed him.
He said: 'It is a good question for him not me. The only thing I can say is that he had one foot out of the club and I brought him back and I fought for him to be paid as a fantastic player like him should be paid.
'But he got injured and a kid 13 years younger (Raphael Varane) than him came in and I felt this other player deserved to stay in the team and he (Pepe) did not take it well. And then suddenly all the people that had done nothing but criticize him before were on his side (against me).'
Back home: Ronaldo played at Old Trafford in the Champions League this season
Sweet spot: In his time at Manchester United, Ronaldo won three Premier Leagues
Ronaldo has indicated he will not renew his contract at Real Madrid beyond 2015.
Real are determined not to sell the Portuguese this summer but United and PSG remain keen when he does come available.
Alex Ferguson sold Ronaldo to Madrid in 2009, but the 28-year-old has admitted several times in the past few months that he is not totally happy in the Spanish capital.
Portuguese newspaper 'A Bola' claimed that the Portuguese starfeels he has not been treated well by the Real board despite his excellent performances on the playing field.
'A Bola' also stated that Ronaldo has reportedly been offered a €60 millionsigning-on fee if he becomes a free-agent at the end of his spell at theBernabeu and signs for a certain newly-made-wealthy European club.
Looking for a way out: Pepe is being targeted by Manchester City
Madrid President Florentino Perez had said that he expected Ronaldo to end his career at the club, but it now appears he could be looking for a new club in the next two years.
If Ronaldo is true to his word, he would be leaving on a free, not something Madrid are likely to want after having splashed out £80 million on him.
Whether he would move back to United now their manager has changed is yet to be seen, but he could emulate former boss Jose Mourinho by going back to a club he knew appreciated him completely.
United are also considering a move for PSV Eindhoven's £25m-rated midfielder Kevin Strootman.
The Holland U21 international had been on Everton's wishlist this year.
Manchester City are ready to step up interest in Ronaldo's team-mate Pepe over the next week.
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