The Gunners are working on a budget and have apparently looked to Germany as a hive of reasonably priced talent, report Bild.
Demirbay is a Borussia Dortmund youth product but never played for BVB, and since then the 25-year-old has cut his teeth in the Bundesliga with a number of clubs.
The 25-year-old has four goals and eight assists from midfield this season, and has turned out five times in the Champions League for Hoffenheim this term.
Demirbay is German-Turkish, like the Gunners' highest earner Mesut Ozil, and has won two caps for Die Mannschaft since 2017.
Arsenal will reportedly face competition from Galatasaray and Besiktas for Demirbay, who has a €30m release clause.
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