Rumours suggested that the Gunners were going to sign the England international on transfer deadline day with Alexis Sanchez going the opposite direction, though in the end nothing materialised.
Pep Guardiola was not interested in letting Sterling leave the club and City offered the Gunners' a sum of money worth an estimated £60 million.
Sterling said: "I didn't need to speak with him (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.
"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."