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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.