The 32-year-old is currently on loan at Everton for the remainder of the campaign, but he is unlikely to feature for the Sky Blues again with his contract due to expire in under six months’ time.
Barry is now free to discuss a Bosman move to other sides, which has alerted Arsene Wenger.
The Frenchman is attracted to he experienced former Aston Villa man, and sees him as an ideal option in his current engine room.
It is understood that Arsenal attempted to snap him up on loan last summer, but were thwarted by City’s reluctance to aid a title rival.
Barry himself is keen to keep his options open at the moment, but may be tempted by one last big move to the capital.
Everton are also looking into making the temporary switch a permanent one, however the Gunners’ ability to offer him a greater chance of silverware may be decisive.
The veteran midfielder is also being tipped for an England recall ahead of the World Cup, thanks to his impressive form at Goodison Park.