Hampshire Police said officers were called shortly before 9am on Thursday following reports of a single-vehicle crash near the Minley Interchange. No other vehicles were involved and no injuries were reported.
The driver - confirmed to be a 31-year-old from Berkshire - was arrested on suspicion of driving while unfit, dangerous driving, possession of a Class C substance and failing to provide a specimen. Police confirmed he has been granted bail while enquiries continue.
The incident comes just months after Sterling's departure from Chelsea and an unsuccessful spell with Feyenoord.
The winger joined the Dutch club as a free agent in February 2026 on a short-term deal until the end of the season, but struggled to make an impact.
Sterling made eight appearances and registered one assist during his time in Rotterdam, failing to establish himself as a regular starter, and Feyenoord later decided against offering him a new contract.