Mourinho, clearly emotional after leading Inter to a 2-0 Champions League victory over Bayern Munich in Madrid, is hotly tipped to return to the Bernabeu to take over from Manuel Pellegrini after he failed to win a trophy with Real this season.
"My work is done, I want to win the Champions League with three clubs," Mourinho, who also won the competition with FC Porto, told RAI. "I feel great sadness at possibly leaving, but in my professional life I try to be as cold as possible to find what I need to do next.
"I did what I had to, my work is done, I am in the history of the club and Inter will never be the same again. I don't want to talk too much, as otherwise I'll cry and change my mind. The chances of me leaving are better than me staying, yes. You can say that.
"The president is fantastic, I thank him for all he decided to do. It's not easy to change the coach when you've won the Scudetto. It was also a risk for me, as if I didn't at least win theScudetto my career could end with the way the media treated me.
"I have won everything I could win and if my decision is what I think it will be - not 100% yet, but I've got a good idea - I am going after something that gives me great motivation. I am one of the only coaches to have won the Champions League with two clubs, now I would like to be the first who does it with three.
"I never really say goodbye. Returning to Stamford Bridge made it feel like home and I will always feel at home at San Siro. I have been very happy here, not so much in Italian football, as I don't like presidents saying their coaches are better or the way the media have treated me.
"I want to run a risk. If I come to Spain and play against the super Barcelona, it is an enormous challenge and if I do come to Madrid it is to try and win a third Champions League. I don't tend to stay long at clubs, as I always want to risk and try for something more, so I have to chase a new ambition.
"I want to point out I have not spoken to anyone from Real Madrid, nor do we have a deal. They are the only club that can tempt me away and give me that new challenge. I reserved the right to take a few days and make my own decision on my future.
"I thank Italian football for what it has done for me. It is very difficult, every game is tough and the atmosphere is not easy for the manager of a big club, while even the media forced me to be better by keeping me under pressure for 24 hours a day.
"I thank Italian football, as all this made me a better coach now than I was when I got here.
"For the last three or four months I have been considering my next step and after this final, the important thing is that Inter keep hold of Massimo Moratti, Javier Zanetti and Samuel Eto'o."