The Spain international has been linked with a return to his homeland this summer, with City looking to generate transfer funds ahead of the reported capture of Eliaquim Mangala from Porto.
The 28-year-old has been mooted as a target for Atletico Madrid, though he has now moved to underline his commitment to the Premier League Champions.
"I don't want to leave City," Negredo is quoted as saying by Sky Sports News. "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."
Negredo netted 23 times in all competitions in his first season in English football.