According to Bild, Arsenal are one of several clubs interested in the €35m-rated Ivory Coast international.
Signed from Lens in 2016, Gbamin is now a regular starter at Mainz and has played 25 times in the Bundeliga so far this season.
His solid performances have reportedly attracted decent interest from English clubs - most notably Arsenal.
Unai Emery is keen to improve the Gunners' defence and the club have also been linked to Samuel Umtiti of Barcelona.
The 23-year-old Gbamin, however, could be a much cheaper and more realistic long-term fix for Arsenal, who work within a strict budget.
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