The Portugal international has been linked with a move away from the Bernabeu in recent months.
Ronaldo, 32, told Real he wanted to quit the club last summer but a deal wasn’t agreed.
And according to Spanish transfer outlet Don Balon, Ronaldo still wants to leave Real.
They add that Chelsea have made their interest known and the Real attacker fancies a move to Stamford Bridge.
Ronaldo reportedly feels the Blues is the best offer he currently has on the table, especially considering Manchester United are not interested in re-signing him.
Don Balon add that Chelsea owner Roman Abramovich is desperate to make a marquee signing in the summer.
Abramovich is even willing to use Eden Hazard in a possible deal to land Ronaldo at the end of the season.
Real are huge admirers of the Chelsea ace, who was tipped to join the Spanish champions last summer.
And Hazard could be used as a makeweight in any deal.
Speaking about Ronaldo’s future at Real, Zinedine Zidane played down any chance of his star leaving. He said: "I can't imagine a Real Madrid without Cristiano, not at all.
"He's a Madrid player and he wants to finish his career here. I don't see him playing anywhere else."
Ronaldo has previously stated he’ll never play for another English club following his time spent at United.
Speaking about his future, the Portugal ace said: “Everything is open, all leagues. I may end my career here with Real Madrid. I'm just being honest. I don't know what's going to happen tomorrow.
“There are things that you kind of already have an idea, that to play one day for Barcelona would be almost impossible, or to play for another English club other than Manchester, it's very complicated.
“But that's not 100 per cent guaranteed. As I said before, there are no certainties in football.”