The alleged incident occurred on Friday night in Highgate, north London.
A Metropolitan Police spokesman said: "Police were called at approximately 7.18pm on Friday 21 February to reports of an alleged collision between a vehicle and a member of the public in Sheldon Avenue N6.
"The member of the public, a man in his 30s, sustained minor injuries.
"Officers have spoken to the driver of the vehicle."
The spokesman said inquiries were continuing and no arrests have been made.
Germany international Ozil joined Arsenal for a club-record fee of £42.5million from Real Madrid last September.