The 32-year-old England international was a member of the Aston Villa team which lost the 2000 FA Cup final 1-0 to Chelsea but he tasted Wembley glory with City when they beat Stoke in 2011 to end a 35-year wait for a trophy.
Barry is now hoping to add a second FA Cup winners' medal to his collection with a victory over Wigan on Saturday.
He said: "It's fantastic. This is exactly why I made the tough decision to leave a club (Aston Villa) after so long to be playing in games like this more regularly. Hopefully we will have another trophy.
"I'm obviously really looking forward to it. It is the FA Cup final - every year it is a fantastic day.
"It was one that as a young kid growing up you look forward to watching so to be part of it, I'm really looking forward to it."
Barry's partnership with Yaya Toure in midfield could be one of the keys to success for City.
Toure has been passed fit to play after being withdrawn at half-time at Swansea last weekend due to fatigue and then missing the midweek game against West Brom.
Barry said: "Yaya is a worry for the club when he goes off so close to a big game but he has trained the last two days and had a little run-out so it will be a big plus if he is fit."