Belgian star Courtois will sign a six-year contract at the Santiago Bernabeu, however, Navas has no plans to leave Madrid.
"Of course, and I say this with force, I have the same desire to leave that I have to die," Navas told the Onda Cero programme.
His future has always been speculated amid Madrid's pursuit of Manchester United keeper David de Gea, and only a famous fax machine mistake helped the veteran play a key role in the capital as the club's move for the Spaniard collapsed.
Navas, to his credit, took over the job and has found resounding success along the way.
The 31-year-old has won three Champions League and FIFA Club World Cup trophies, two UEFA Super Cups, a La Liga and Supercopa de Espana title since taking over for club legend Iker Casillas.