The 24-year-old has enjoyed another outstanding season with the Seagulls, scoring once in 31 Premier League appearances.
According to the Daily Star, the Gunners believe they are in the lead for signing Bissouma, but the Seagulls are reportedly demanding a fee somewhere in the region of £ 30million for the Mali international.
The report adds that Arsenal boss Mikel Arteta has identified Bissouma as a potential summer signing, but they will have to repel interest from other English clubs like Everton, West Ham United and Tottenham Hotspur.
Premier League champions Liverpool have also been credited with an interest in Bissouma as they prepare for Georginio Wijnaldum’s departure this summer.
Bissouma has a contract at Amex stadium until the summer of 2023.