The 28-year-old joined the Premier League champions from Sevilla last July but has been linked with a move to Atletico Madrid this summer.
Negredo scored 23 times in all competitions last season, although he will head into the new campaign following a run of 16 appearances without a goal.
"I don't want to leave City," Negredo told the club's official website.
"I'm very happy and very settled here. I had a difficult end to the season and that's why there has been a lot of talking but I've been very happy here from the first day I arrived."
When asked if he was homesick, Negredo replied: "No. Maybe a bit more on the personal side than when we talk about football but I don't cry easily.
"I am sensible but I have to love that person a lot to feel homesick."