The Gunners have been linked with an approach for the Brazil international in the past with the Catalan giants keen to raise funds from his sale.
However, as well as no team being prepared to take on the 29-year-old's wages, a knee injury kept Coutinho out for the second half of last season.
According to Le 10 Sport, Arsenal are willing to hold discussions with Barcelona as they look for a new creative player.
Coutinho would need to prove his fitness after a lengthy spell on the sidelines before the Premier League outfit are willing to push through a permanent or temporary transfer.
The former Liverpool man made just 14 appearances in all competitions during the last campaign.