The 28-year-old Brazilian is not thought to have a future at the Nou Camp after struggling for form since his big-money move from Liverpool in 2018.
He spent this season on loan at Bayern Munich but the German giants are not thought to be interesting in making the deal permanent.
And Barcelona would be willing to let Coutinho go to the Emirates for £9m plus Matteo Guendouzi going the other way.
Guendouzi has not appeared under Mikel Arteta since losing his cool in the 2-1 defeat to Brighton in June, and it is believed the Spanish manager wants him out of the club.
Barcelona are known to be interested in the player, and believe the Frenchman could resurrect his career in Catalonia.