The 49-year-old coach has insisted the next step in his career will be to make a return to English football, where he won two Premier League titles with Chelsea.
But, despite speculation linking him with the United job when Sir Alex retires, the Portuguese refused to reveal who he believes his future employers will be.
"I call [Sir Alex] the boss because he's the boss of the coaches and I hope that when I go back to English football he still manages Manchester United," he told CNN.
"I don't think about [the future], especially as I have a four-year contract with Real, I signed it and when I signed it, I signed it because I wanted to be at Real Madrid at this period of my career and I don't think of another club."
The two-time Champions League winner remained coy, however, on when he would be leaving the reigning Liga champions.
"I just say openly that for many reasons that after Real Madrid, Inter, Italy, Spain, Chelsea, England, Porto, Portugal, that after this project, the next step will be England for many reasons but when I don't know," he added.
And Mourinho further stoked speculation about a possible return to former club Chelsea by declaring that he still enjoys a "great relationship" with owner Roman Abramovich, despite the Russian sacking him in 2007.
"We are in touch a lot and the last example is Michael Essien, who was going to another club and when I [made a telephone call to say]: 'Please leave it to your friend', he left to his friend," he continued.
"We have a great relationship, in fact."