The site includes much of the city's famous waterfront, including the Three Graces - the Royal Liver Building, the Cunard Building and the Port of Liverpool Building - the Pier Head, the Albert Dock and the Stanley Dock Conservation Area.
Det Chief Insp John Coull said the soldier, who was based at Brompton Barracks in Dock Road, Gillingham, was in a drunken state in an area close to the river when he was last seen.
He added that the council planned to install a new sewer system in the waterfront area as part of its redevelopment and that would help resolve the flooding problems in Dock Street.