The France international arrived at the Nou Camp last summer as a replacement for Neymar in a deal worth £135.5m.
But Dembele has struggled with injuries since the move and after regaining fitness he has failed to make an impact at Barca.
The La Liga giants are reportedly keen to offload the 21-year-old as they look to make space in their squad and raise funds to bring in Antoine Griezmann from Atletico Madrid.
And reports in Spain suggest that the Gunners are desperate to bring the flying winger to the Emirates.