The Daily Star says Sevilla finished ninth in La Liga and have accepted the £25m-rated Spanish winger is set to leave.
Brendan Rodgers wanted to take Navas, 27, to Anfield but the star has come out and nailed his colours to the mast.
Navas said: "I like Manchester City a lot and it has great players.
"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."