The Spanish giants have been tracking the stopper for a number of years and came close to signing him in 2015, only for the deal to collapse at the 11th hour.
The 27-year-old has been at Old Trafford since 2011, despite being linked multiple times with a move away, with Real Madrid very interested in his services.
However, with Real Madrid really looking to revamp their team, in light of recent events which see the Los Blancos sit third in the league and a massive 16 points behind league leaders Barcelona.
However, Mourinho ruled out De Gea's exit and said he wanted to bring more players of the Spaniard's quality into the club in the transfer market.
Manchester United manager Jose Mourinho has dismissed speculation linking David de Gea with a summer move to Real Madrid, saying it "makes no sense" for the Red Devils to sell one of their best players. It makes no sense.
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We have to attract the best players like we did with Alexis (Sanchez), (Nemanja) Matic, (Paul) Pogba and so on.
Since then the goalkeeper has continued his rise in the footballing world, establishing himself as one of the world's best players.
Sky Sports also referenced Real's reported interest in Thibaut Courtois-who recently confessed his "heart is in Madrid"-but when asked about his former Chelsea star's situation, Mourinho said: "I don't speak about Courtois".
That's exactly why reports from the Mirror and even Mundo Deportivio are flooding in with rumors that Real Madrid has chose to go after Thibaut Courtois instead.
With the Blues enduring an abysmal run of form, they could lose both Courtois and talismanic forward Eden Hazard in the summer transfer window - if Antonio Conte's side are unable to secure qualification for next season's Champions League.