The United shot-stopper has been a long-term target of the La Liga giants, since his failed switch in 2015.
But while a move which would break the world-record fee for a keeper is in the offing this summer, some Madrid figures are unconvinced.
Reports have claimed captain Sergio Ramos and even manager Zinedine Zidane are backing Navas.
The Costa Rican's future has been in doubt but he has enjoyed an impressive season in helping Madrid clinch the La Liga and Champions League double.
Real Madrid are looking to secure David De Gea quickly from Manchester United this summer
There has been no doubt among Madrid chiefs since March that they would press ahead for David De Gea
It has even been suggested Ramos and Zidane could even intervene over the club's move for De Gea, with others feeling Navas deserves his place in the team.
However, according to Spanish newspaper Marca, despite the support for Navas in the Madrid dressing room, the board's decision will not be affected.
It is said there has been no doubt among Madrid chiefs since March that they would press ahead for David De Gea.
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And United's 26-year-old was apparently prioritised once it became clear Thibaut Courtois would not be leaving Premier League champions Chelsea.
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Marca do not expect anyone inside the Bernabeu to fight the arrival of De Gea either, baring in mind he is Spain's No1.
As a result, it is claimed he and Navas are set to battle it out to secure being Zidane's first choice next term.
Madrid and Manchester United still need to agree on a fee though before the transfer can happen.