He is understood to be in a critical condition.
Strathclyde Police said they had "a positive line of inquiry".
They have not yet confirmed whether the man was related to the children,
Police announced the deaths were being treated as murder following post mortem examinations.
The discovery was made on Crow Road in the East Dunbartonshire town.
The vehicle was moved from the car park at about 2300 BST by a recovery lorry under police escort.
Police dog teams have been examining the scene.
The car park, about ten miles from Glasgow, is close to the Campsie Fells, a popular spot with families and hillwalkers.