Ronan Sexton, 31, suffered a serious head injury in the incident, which happened just after 4am on Sunday.
He was admitted to a local hospital but then transferred to Hurstwood Park neurological centre in Haywards Heath, West Sussex, in a critical condition.
Mr Sexton's mother Bernadette - the sister of Mr Neeson - has reportedly been at her son's bedside.
The accident is the latest upset for Mr Neeson whose actress wife, Natasha Richardson, died in March 2009 at the age of 45 from head injuries following a ski accident in Canada.
Police said there were no suspicious circumstances surrounding the incident.