The England winger was wanted by the Gunners as part of a summer swap deal involving City target Alexis Sanchez.
City are set to revive their interest in contract rebel Sanchez again in January.
But Sterling, 22, has no interest in leaving after pledging his long-term future to Pep Guardiola’s men.
He said: “I signed for five years here. I’ve got two-and-a-half years left, and I see myself here and playing my football here under a great manager with a great team.
“I didn’t need to speak with Pep because I had already spoken to him during the summer about pre-season.
“I didn’t have any negative thoughts or anything bad about it.
“I just woke up one day on England duty and saw it, and I decided I wouldn’t believe a word of it until I heard something from the manager, then I would believe it.
“It wasn’t something I was worried about, because Pep is an honest guy, and he would have spoken to me about it before that.
“So I didn’t need to worry about it, and I didn’t think about it, not for one minute.”
Sterling moved from Liverpool for £49m in 2015 and has blown hot and cold in his two years at the Etihad.
But he has rediscovered his best form after already scoring seven times this season and said: “It’s a massive year for me, for the team, and I need to keep building, keep working hard and go to the World Cup on a positive."
