The Costa Rica international has been at the Bernabeu for four years, and has sported the number one jersey ever since Iker Casillas left for Porto in the summer of 2015.
However, the 2018 World Cup Golden Glove winner's arrival to the Spanish capital on a six-year deal means that Navas is likely to lose his first-team role.
Nevertheless, the 31-year-old has made it clear that he is in no mood to simply step aside for the new boy.
"Of course, and I say this with force, I have the same desire to leave that I have to die," Navas told Onda Cero.
Navas has helped Madrid to three successive Champions League trophies during his time at the Bernabeu, as well as a La Liga title, a Supercopa de Espana and three FIFA Club World Cups.