Ibrahimovic, 35, has been a revelation in his first season in England, scoring 20 goals, and is expected to trigger the option of extending his contract by a year.
Napoli and clubs in China and the United States have been linked with the former Paris Saint-Germain striker in recent days, but Mourinho is confident he will remain in United next season.
“I'm totally convinced he is going to stay,” Mourinho told reporters at United's training base west of Manchester.
“He came with the intention to stay two years, but in the minds of everyone the first year is going better than every expectation.”
“He knows 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 adapted to the club, to the situation. I don't see any problem with his family. I gave him the possibility of a day off to go to Sweden. He doesn't want (it). So I'm totally convinced he is going to stay.”
While rivals such as Manchester City are expected to make significant moves in the next transfer window, Mourinho said he intends to keep his squad largely as it is.