Mourinho said United were open to a move for the keeper but clubs had withdrew their interest.
"I can guarantee that he is not going this season," Mourinho told reporters in San Jose ahead of Sunday's pre-season International Champions Cup match against Real Madrid.
"My feeling is it will very difficult for him to go. He is a very honest, straight boy. He was contacted for a long time, the club was closed and then we opened. I always have this feeling when a player has a desire to go, then I don't like to stop players...
"So we opened it and then they decided to close it. I see him really happy, focussed, working better than ever and 100 per cent he stays with us."
United playmaker Ander Herrera stressed the importance of his Spanish team mate, whose deadline-day deal with Real Madrid collapsed in the 2015 summer window.
"If you lose the top three in any position, like David is... it is a great loss," Herrera told British media.
"We don't want to lose them... For me, he's the best in the world, so I want to keep him here at United.
"He is a goalkeeper who can give you points. That is very important. I want to keep him here, to play with him, because he's a fantastic keeper and also my friend, and I think you can see he's very focussed on Manchester United."
(Reporting by Aditi Prakash in Bengaluru; editing by Amlan Chakraborty)
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