The former Liverpool man is back in Barcelona under the tutelage of new manager Ronald Koeman, but Coutinho's future at Camp Nou is still shrouded in uncertainty.
The playmaker enjoyed a fruitful 2019-20 campaign on loan at Bayern Munich - registering 11 goals and nine assists as Bayern lifted the Champions League trophy - but the Bundesliga giants ultimately decided against making his stay in Bavaria permanent.
According to Sport, Arsenal boss Mikel Arteta is still keen to add reinforcements to his midfield ranks, and the Spaniard is a big fan of Coutinho.
The report claims that Koeman is willing to hand Coutinho a new lease of life in Catalonia, but the Gunners are confident of completing a deal due to Barcelona's need to balance the books.
The Gunners continue to be linked with Lyon's Houssem Aouar and Atletico Madrid's Thomas Partey, but deals for both midfielders are looking increasingly unlikely with the transfer window set to shut on October 5.
Coutinho is contracted to Barcelona until 2023.