Reports of a possible shock switch to the Emirates gathered pace on the final day of the summer window, with City rumoured to be willing to use Sterling as a makeweight in any deal to sign Alexis Sanchez.
No agreement ever materialised, though, and Sterling is confident that there was no truth to the rumours to start with.
"I didn't need to speak with [Guardiola] 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 with England and saw it, and I didn't believe a word of it until I heard something from the manager, then I would believe it," he told reporters.
"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. He's been massive for me, especially with the simple stuff.
"He always tries to get you to do the simple stuff at the top level and that is the real genius thing about him. He makes sure you do the simple things and it works. 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."
Sterling has already scored seven goals for City this season, including one during the 7-2 rout of Stoke City on Saturday.