The Bundesliga champions are reportedly monitoring the £42.4 million man.
According to the London Evening Standard, the German champions are keeping tabs on the 25-year-old, who has endured a mixed career at the Emirates Staduim to date.
Ozil signed for the Gunners last summer for a club-record fee of £42.4 million but has divided opinion ever since moving to north London.
Some say the subtle nuances of the German's game are too difficult for critics to appreciate, while critics instead point to the enormous success someone like Cesc Fabregas has already had at Chelsea, compared to Ozil's slow rate of goals and assists by comparison.
So should Arsenal consider any bid from Bayern?
Ozil began his career in the Bundesliga, starting out at Schalke 04 before joining Werder Bremen. A return to Germany, especially under Pep Guardiola, may be the perfect union considering the 25-year-old's passing game. The move would certainly bare parallels with Xabi Alonso's summer switch from Real Madrid.
If a concrete offer did come through, though, many Gunners fans - and perhaps Arsene Wenger himself - would be dismissive. It would take a huge bid for Arsenal to recoup the £42.4m they paid for Ozil and the German is showing signs of delivering again when he is played in his favoured no.10 position.
But could his head be turned by Bayern's reported interest? It is an interesting point of debate...