United had been keen on Alvaro Morata, but Mourinho recently revealed Real's demands scuppered any chance of a deal, per David McDonnell of the Daily Mirror.
The Spain goalkeeper nearly moved to Madrid two years ago, but the move collapsed on deadline day. However, transfer speculation has persisted over the past couple of seasons.
When quizzed on the Spaniard's future, he said: "I can guarantee that he's not going this season".
And Mourinho, who was speaking at a media conference in Santa Clara ahead of Sunday's International Champions Cup clash, ruled out De Gea's potential departure and suggested the chance of a move to Old Trafford was extinguished.
"But from distance, it is easy to feel that I repeat the same, the market is very hard".
"He is honest, he is very straight".
"He was contacted for a long time, the club was closed, then we opened, because I always have this feeling when a player has a desire to go, I don't like to stop them because, in the end, you don't get what you expect.
So, we opened it and they [Real] chose to close". For me, he's the best in the world, so I want to keep him here at United. And I don't think the feeling for him [towards Madrid] is very, very good. Once he starts bullying defenders, as well as beating them for speed and skill, we'll be talking about a world-class player.
Mourinho admitted defeat in his attempt to sign Cristiano Ronaldo from Madrid last week, stating that it was the "impossible mission", and the Portuguese feels that he faces a similar task persuading teammate Bale to swap clubs this summer.
Argentina goalkeeper Sergio Romero had De Gea hard last season and was preferred for the Europa League final win against Ajax.