The youngster was approached in Chapel Meadow, New Longton, near Preston, as she walked home from All Hallows Catholic Secondary School, Penwortham.
The driver showed her a laminated card and claimed to be a police officer.
She declined his offer of a lift and walked off.
Today Lancashire police urged youngsters and their parents to be vigilant.
The girl’s father said: “The vehicle pulled up and he said ‘I’m a police officer – let me give you a lift home.’
“He showed her a card of some sort.
“She was quite shaken up with this. She is a sensible girl and knows not to get into a car with a stranger.
“The school has been informed – everyone needs to be careful”.
Lancashire police said the incident happened at around 5.30pm on Wednesday.
A man pulled up in a vehicle and offered her a lift.
He produced a laminated card and said he worked at Police HQ.
She refused to get into the vehicle.
The suspect is described as white and in his late 40s and driving a van.
A Lancashire police spokesman said: “We would ask people to be vigilant but not alarmed. Report any suspicious activity to us.
“We would remind youngsters that they should never get into any vehicle with anyone they don’t know.”