Barry is currently on-loan at Everton and comes off contract in June.
The Manchester Evening News says City are looking into the possibility of the 32-year-old launching a new chapter in his Blues career at New York City FC.
The franchise will launch in the 2015 season which starts in 13 months.
Sending Barry, who would be a likely captain, would show the world that the fledgling club means business.
He would no doubt become a contender to captain the side, which will be lead by head coach Jason Kreis.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball