The 35-year-old Frenchman decided to hang up his boots once and for all at the end of the 2010-11 campaign, with his final appearance for Roberto Mancini's side coming in the 1-0 FA Cup final victory over Stoke City at Wembley last May.
Following his retirement, Vieira was heavily linked with a return to the Emirates Stadium to take up a coaching role behind the scenes under Gunners boss Arsene Wenger.
However, the Senegalese-born star, who enjoyed nine successful seasons at Arsenal prior to his move to Juventus in 2005, shunned the opportunity to rejoin his former club, and insists he is happy with the decision.
"I don't miss playing at all, I feel like I have done all I can do," Vieira told the People. "I'm often asked why I stayed at Manchester City instead of getting involved at Arsenal.
"People may have difficulty understanding, but this is a continuation of what I did for two years here as a player.
"The club has opened its doors to me, shown me respect and taken into consideration all my experience.
"Since I left Arsenal, I always had a very good relationship with Arsene Wenger, but I never received a proposal from them.
"With City, it was done without pushing things and it was the proposal that I wanted. It was a pretty easy decision to work for the club."