The 27 year old now needs to pass a medical after Sevilla confirmed that they have accepted an offer for the player.
Navas would become the first signing of manager-elect Manuel Pellegrini at the Etihad Stadium.
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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.