The German international became the Gunners' record signing last summer when he moved from Real Madrid for a fee of £42.5m.
However, despite starting brightly, the 25-year-old has largely failed to hit the heights of his early promise in an Arsenal shirt over the last few months.
Ozil has come in for criticism from certain quarters for his performances, and the Russian side are said to be preparing a big-money move this summer, according to The Metro.
The interest was said to have been revealed to a Russian website from Zenit president Alexander Dyukov in an 'off the record' comment.
Ozil is currently sidelined with a hamstring injury.