The Iona I, once a passenger ship that sailed between Glasgow and the Highlands, was bought by the Confederates to deliver supplies to blockaded American ports.
But it never got to fulfil its mission after sinking in the Clyde near Gourock in 1862 following a collision with another ship.
The Scottish Government has suggested the wreck should be legally protected as a historic asset of national importance.
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Historic Environment Scotland has begun a public consultation on whether the site should be designated a Historic Marine Protected Area.
The wreck of Iona I is in good condition but several artefacts have been taken from the ship’s remains by divers.
The new designation would give it legal protection against salvage hunters.
Andy Fulton, senior designations officer for Historic Environment Scotland, said: “The Iona I has a wonderfully colourful history, initially operating as a paddle steamer before being refurbished as a blockade-runner in the American Civil War, although sadly the steamer never made it out of the Clyde, where it was built.
“The wreck is in pretty good condition but as with all marine archaeological sites it is deteriorating, and unfortunately some artefacts have already been removed by souvenir hunters.
“Proposing the wreck for designation as an HMPA, will provide legal protection to prevent salvage activity, and will help to recognise this nationally important piece of maritime heritage.”