The Switzerland international was stripped of the captaincy earlier this season by then-manager Unai Emery, after swearing at fans during a game against Crystal Palace.
The incident occurred after Xhaka was booed off the pitch as he was substituted, and his future at the Emirates has been in doubt ever since.
Sky Germany reports that Hertha Berlin could offer Xhaka an escape route in the mid-season transfer window.
Hertha boss Jurgen Klinsmann is on the hunt for a holding midfielder and has targeted the 27-year-old.
The Bundesliga outfit are hopeful that they can convince Xhaka and his employers of the move with a “financially sensible package”.
The midfielder, who played in the German top flight with Borussia Monchengladbach between 2012 and 2016, is said to be open to the move after a disappointing campaign in north London.
Mikel Arteta is expected to be announced as the new permanent Arsenal boss after Emery was sacked last month.
The Gunners are currently 10th in the Premier League table and have picked up just one win in their last 12 games in all competitions.
They sit seven points outside the Champions League places, with just five victories in 17 league games this season.
Xhaka, who joined the club from Gladbach in 2016 for a reported £35 million, has made 14 appearances this season.
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