The defender, who also skippers the Welsh national team, has been repeatedly linked with a move away in recent years, with Liverpool, Napoli and Arsenal among the clubs reported to have shown an interest.
"I can't see myself playing for anyone else to be perfectly honest," Williams is quoted as saying by BBC Sport.
"I'm very comfortable here in the city, I love the club. I know it, the way it works and it knows me.
"And I don't have any other thoughts of any other team in the Premier League to be honest
"All I care about is doing the best for this team."
Williams will win his 50th cap when Wales take on Israel on Saturday.
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