After a poor campaign in La Liga, Real are said to be ready to reshape their squad ahead of next season and reports have suggested that the club are in the market for a goalkeeper.
Manchester United's David de Gea, Chelsea's Thibaut Courtois and Roma's Alisson have all been linked with a switch to the Bernabeu, but Perez has suggested that the La Liga giants will keep faith with Navas.
Speaking with Navas at a fans event, Perez said: "We are proud to have you as our goalkeeper, whatever some people say. Work hard and, for sure, you will be with us for many more years."
The Costa Rican stopper has made 136 appearances in all competitions since joining Real in 2014.