Coutinho wants to return to English football and Barcelona are desperate to offload him in order to ease some of the pressure on their wage bill.
The Brazilian spent last season on loan at Bayern Munich, but the German champions opted not to trigger a purchase option to keep hold of him.
His agent Kia Joorabchian is fishing for a new club for his client and the midfielder has been offered to Arsenal this summer.
The Gunners have been heavily linked, but the Brazilian is not at present a player they are looking to sign.
It remains to be seen if Arsenal rethink their stance on the attacking midfielder later on in the transfer window, which is due to run until 5th October.
Coutinho’s wages could be a problem for Arsenal, who are struggling with their finances this summer.
They want to bring in a defensive midfielder and Atletico Madrid’s Thomas Partey continues to be their top target.
Arsenal are also interested in bringing in a centre-back, but would have to move out one or two bodies before they can bring in someone new.