The Liga club announced on their website that the 27-year-old will move to Etihad Stadium subject to a medical, whilst the fee is believed to be in the region of €25 million (£21.3m).
|9/4||Manchester City are 9/4 with Coral to win the Premier League next season
Navas also added fuel to the speculation, recently admitting his admiration for the club.
"I like Manchester City a lot and it has great players," he told reporters.
"I'm open to anything. I want to win more and reach my goals. Manchester City has done all it can to bring me in and I have to be grateful for that.
"I want to go on and win trophies."
Navas has spent his entire career at Sevilla, making his debut in November 2003. He played 393 times for the Andalusian side, winning two Uefa Cups, one European Super Cup, two Copa del Reys and a Spanish Super Cup.