Sources in Spain have confirmed that the Gunners have the first option on the midfielder should he leave the Nou Camp.
He has had a poor season and has been singled out for criticism for their humiliating exit from the Champions League.
Club president Sandro Rosell said: “We need changes in our squad but those will not come until the end of the season.”
Cesc, 25, is trying to buy an expensive London flat and a return to Arsenal would suit his family, who are still based in the capital.
The Gunners are still owed money as part of his £35million transfer in 2011.
Barcelona have paid off the transfer fee but still owe around £5m in extras.
Will Arsenal's board spring for Cesc's return? Give us your shout below...