Demirbay's performances have attracted interest from clubs across Europe this season, with the 24-year-old having registered two goals and four assists in his 18 league and Europa League appearances.
Demirbay's form earlier in the year also earned him a maiden call-up to the Germany squad, winning his first two caps and scoring his first goal for his country in June.
Everton have previously been linked with the midfielder, and Newsmondo now reports that Arsenal could rival the Toffees for his signature this month.
The Gunners are looking to bolster their midfield options given the uncertain contract situations surrounding Alexis Sanchez, Mesut Ozil and Jack Wilshere, while the likes of Aaron Ramsey and Santi Cazorla are currently sidelined through injury.
Demirbay has helped Hoffenheim to seventh in the Bundesliga table so far this season, just two points off the Champions League places.