The veteran midfielder made his 500th appearance for the club in last night's defeat to Cadiz.
Navas stated today: Sevillistas, today I informed the club and my teammates of the decision to leave.
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"It has been a very difficult decision. I wanted to thank Sevilla, the fans for the affection they have always shown me.
"I have lived the best moments of my life at Sevilla and I want to thank everyone from the bottom of my heart."
A move to Saudi Arabia is mooted for the 38 year-old midfielder.