Gunners boss Unai Emery is in the market for a defensive midfield signing and RMC says his search has led him to Gbamin.
Gbamin left Lens for Mainz two years ago and the Ivory Coast international's development has accelerated in Germany.
Arsenal have been informed it will take €30m for Mainz to part with the 22 year-old midfielder.
Mainz chief Rouven Schröder conceded: "It is clear that such players arouse interest in larger clubs. As Mainz 05, we always have to be open to corresponding lucrative offers. That's why we get such potential players signed up."
Gbamin is tied to Mainz until 2022.