Scott Allan, a midfielder for West Bromwich Albion, is believed to have hit a pedestrian with his luxury car.
Police confirmed that an Audi Q7 struck a pedestrian at Waverley Road, Portsmouth at 8.50pm on Friday.
The injured man remained in a critical condition at Southampton General Hospital on Saturday.
A police spokesman said the driver of the car was spoken to at the scene but is not being investigated nor are any charges expected to be laid.
Police are also not seeking witnesses to the incident, he said.
Allan, 20, plays for the Scottish international team and lives in Glasgow.
Currently he is on a one-month temporary loan to Portsmouth FC.
Comment is being sought from Portsmouth FC.
Allan played football for Portsmouth against Notts County today but was sent off.
Portsmouth FC media manager, Neil Weld, said: "We know there has been an incident that took place last night but the club cannot currently make any further comment on that."