French international Fekir was previously linked with a move to Liverpool during his time at Lyon before eventually joining the La Liga giants in 2019.
However, according to reports from Mundo Deportivo, Gunners boss Mikel Arteta is hoping to lure him away from Andalucia ahead of the 2021/22 season, with a €45m offer.
Arteta is set to undertake a major rebuilding project at the club including a number of new faces arriving at the Emirates Stadium.
Real Madrid pair Dani Ceballos and Martin Odegaard are unlikely to make their loan move to North London into permanent switches this summer, meaning the Basque coach will need to look elsewhere for targets.
Fekir has impressed in flashes during his time with Real Betis, but the 27-year old has netted just 10 goals in 63 appearances in all competitions during his time in Spain.