The 27-year-old, who has spent his entire professional career at Sevilla, is set to undergo a medical with City where, should he complete his transfer, he will join fellow Spain World Cup and European Championship-winner David Silva.
A statement on the Sevilla website read: "Sevilla FC has accepted the offer of the English club, taking into account the will of the player, and he will undergo a medical."
No fee was mentioned by the club, but reports Monday morning suggested a deal could be worth up to £24million.
Navas has plied his trade at the Ramon Sanchez Pizjuan since making his debut back in 2003.
In that time he has won two UEFA Cups and two Copa del Rey titles, as well as being part of the Spain squads that won the 2010 World Cup and Euro 2012.
He will also join Silva in the squad for the upcoming Confederations Cup, which begins in Brazil later this month.
His international career was delayed because of panic attacks he suffered as a younger player when away from Seville, a problem he has since overcome.
He will join a club in City who are yet to confirm their new manager following the departure of Roberto Mancini, though the appointment of Manuel Pellegrini is widely thought to be imminent.
Pellegrini will certainly know plenty about Navas having spent the last decade in Spain, at Villarreal, Real Madrid and Malaga.