The Portuguese tactician guided Inter Milan to a remarkable treble last season, clinched by their Champions League final victory over Bayern Munich.
But he is set to be named the new manager of Real Madrid next week, following the departure of Manuel Pellegrini.
The soon-to-be Los Merengues boss has already revealed he would love Liverpool and Chelsea midfielders Steven Gerrard and Frank Lampard to join him at Madrid, and has now shown his admiration for Rooney.
However, Mourinho admits Manchester United manager Sir Alex Ferguson would never let the star forward leave Old Trafford.
"I'll say it is impossible," he told AS.
"I would like to coach Rooney but my friend Ferguson can rest easy - it is impossible."