The Manchester United goalkeeper is among the top transfer targets ahead of the summer at the Bernabeu.
And Madrid are determined to get a deal over the line, having failed to do so two years ago.
Current No1 Navas has kept his place in a successful season for Madrid.
The La Liga giants have already clinched the title, and still have the Champions League final against Juventus to come.
But Zinedine Zidane is looking for an upgrade on the Costa Rica international, with president Florentino Perez keen on De Gea as a marquee addition.
However, the United shot-stopper is not forcing through a move, and has now apparently given Madrid a further headache over a transfer.
Keylor Navas wants to stay at Real Madrid despite their desire to sign David De Gea
David De Gea has told Madrid they must first get rid of Navas
According to Spanish outlet Diario Gol, De Gea will not make the switch if he has to compete for his position.
He is already assured of his spot at Old Trafford, with United having now secured a return to the Champions League too.
And it is said David De Gea has told Madrid they must first get rid of Navas.
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Manchester United keeper David De Gea does not want to have to fight for his place at Real Madrid
The issue for the Spanish giants is that Navas has no intention of leaving.
The keeper has already publicly declared his desire to stay at the Bernabeu, meaning Madrid may yet have to convince him to go.
De Gea’s move could therefore be held up, and that may scupper a deal as the United man reportedly wants a deal to go through quickly.