The 32-year-old secured a five-year contract when he arrived from Aston Villa in 2009 and has been an integral part of City's engine room.
His tenacity and energy was a huge reason why his team won the Premier League last season and staying at the Etihad Stadium beyond the summer of 2014 is a big ambition.
"I am happy here and very settled," said Barry. "I spent 12 years at Villa and I've spent four years at City and I'm not really one for moving around.
"I'd like to stay as long as possible. For a player to feel settled and feel very comfortable, you generally want to be playing regular football.
"I've been lucky enough to feature in a lot of games this season. That's one reason why I am happy to stay."
There are likely to be few players assured of their City future at the end of the current campaign, as they look set to see their league title defence end in failure with fierce rivals and neighbours leading the table by 13 points.
"I am sure decisions will be made over the summer," added Barry.