Mourinho opened the door for a possible move to Stamford Bridge for Rooney yesterday.
He said: “I like him. He is at a fantastic age.
“He has maturity, big experience and is still young. It’s up to him and what he wants, what makes him happy.”
Rooney, 27, is due to have talks with new Old Trafford boss David Moyes over his future following Alex Ferguson’s retirement.
But it is understood he is interested in what Chelsea have to say, says The Sun.
Mourinho added: “He’s a little bit like me. He doesn’t need one more pound in his contract and one more cup won’t make a difference. Be happy.
“Where is he happy? Where will he find more happiness to have ambition and drive him?”