The Frenchman's future has been the subject of much speculation, with Paris St Germain the latest to be linked with a summer move.
Mourinho was unequivocal recently when asked about David De Gea's future, saying there was 'no chance' the goalkeeper would be leaving. He did not speak with quite the same conviction about Pogba but insisted, at the moment, there are no signs he will leave.
The United boss said: "I think he's going to be here next season. That's my feeling. I can give the guarantee that I don't want him to leave, that the club doesn't want to sell him, and I can give you the guarantee that we don't have any approach from him or his agent or from any club. In this moment, for me, he's staying, yes."
While Mourinho wants to keep Pogba, he revealed there are players within his squad he does not believe are up to United standards but who he accepts will be staying.
"Some of the people we have, they have to be more consistent in their performance and we need more quality," he added.
"I trust some more than others that can bridge that gap. Some of the players I am totally convinced are going to make it, some others I have good hopes that they are going to make it, and some others I don't believe they are going to make it."