The 35-year-old became the first United player since Sir Alex Ferguson's retirement to reach 20 goals.
"I'm totally convinced that he is going to stay," Mourinho said. "He came with the intention of staying two years.
"The first year is going - probably not in his mind because he is a very ambitious guy - better than every expectation.
"He knows that we are going to try again to improve next season and try to share with him in a fantastic way probably the last year of his career at the highest level, so I'm convinced that he's staying.
"He's also adapted to the club, he's adapted to the situation. I don't see any problem with his family.
"I give him the possibility of an extra day off to go somewhere, to go Sweden - he doesn't want, he never goes. Everything is stable with him, so I'm totally convinced that he is going to stay."