The incident took place between 9.45am and 10.45am today, Thursday, May 12, on Melrose Road.
The man is described as being late 20s/30s, with ginger hair and a beard, wearing a light blue T shirt.
Police Sergeant Dale Hadden of Galashiels Police Station said: “We think the vehicle was a white jeep style car, possibly a Nissan. The vehicle was travelling east from Galashiels in the direction of Gattonside.
“The girl was shocked but unhurt by the incident. Nonetheless, officers want to speak to the driver of the car to establish the circumstances.
“I would ask that anyone who was in the area around that time and saw the vehicle, to get in touch with us, also if anyone has dash cam footage that could assist our enquiries we would like to hear from you.”
Anyone with any information that may be useful should contact Police Scotland, on 101 quoting 1001 of Thursday, 12 May, 2022. Alternatively information can be passed anonymously via the charity Crimestoppers on 0800 555 111.