The Spain international has been heavily linked with a move to Real in recent months.
De Gea, 27, nearly joined the Spanish giants in 2015 but a late fax stopped the move.
Real were expected to make a bumper bid for the goalkeeper at the end of the season with Florentino Perez desperate to land a new No.1 to replace Keylor Navas.
However, according to Spanish outlet El Confidencial, De Gea sees his future at United.
The Spain star has told Real he feels valued under Jose Mourinho and he will not leave Old Trafford in the summer, even for a bumper pay rise to head to La Liga.
Real could now target Chelsea shot-stopper Thibaut Courtois, who is also a long-term target for the Spanish champions.
The Belgium international’s Blues future is up in the air with a new contract yet to be agreed.
De Gea and United are back in action on Friday night when the Red Devils host Derby at Old Trafford in the FA Cup.
Mourinho’s men come into the clash on the back of their impressive 2-0 win at Everton yesterday.
Anthony Martial and Jesse Lingard netted to sink Sam Allardyce’s men at Goodison Park.