The incident is alleged to have taken place on Waverley Road, Portsmouth at 8.50pm on Friday evening.
The injured man is currently in critical condition at Southampton General Hospital.
Allan, who is on a one-month loan at Portsmouth, is not being investigated over the accident, and it is not expected that any charges will be laid.
"We know there has been an incident that took place last night but the club cannot currently make any further comment on that," said Portsmouth media manager Neil Weld.
Allan, 20, played in today's FA Cup tie against Notts County but was sent off.