The Spanish midfielder spent five years as a player at the Emirates, and after it was revealed that Arsene Wenger would be leaving the club he became a favourite to take over the job.
His working with renowned coach Pep Guardiola was a major reason for him emerging as a favourite for the job, after spending two years as assistant coach at Man City.
Despite the offer, Arteta opted to stay as Guardiola's number two, and has revealed that he in no way regrets the decision.
"In football, it is so hard to predict things. When things happen, you have to make decisions and sometimes you don't have time to make decisions.
"The decision was made and I am so happy. I am very privileged to be where I am."
Man City will take on Lyon in their first match of the Champions League this season on Wednesday night.