The Spanish galleon "San Jose" was the main ship in a fleet carrying gold and silver -- likely extracted from Spanish colonial mines in Peru and Bolivia -- and other valuables back to King Philip V.
It sank in June 1708 during combat with British warships attempting to take its cargo, as part of the War of Spanish Succession. Only a handful of the ship's crew of 600 survived.
President Juan Manuel Santos wants to form a public-private partnership to retrieve the shipwreck items, and build a museum for the recovered pieces and a laboratory to study and conserve the material.
The scientific and legal parameters to join the partnership will be made public Friday at a hearing in the Caribbean city of Cartagena.
Colombia has not set an official value to the wreck, but experts in 1980 estimated that the treasure was worth some $10 billion.
Treasure hunters have long searched for the "San Jose," described as the Holy Grail of shipwrecks.
Santos gushed soon after the wreck was discovered in November 2015 that it was "the most valuable treasure found in the history of humanity."
The government says there is no pending litigation over the wreckage or the galleon's loot, even though Spain insists it is the rightful owner because the "San Jose" was Spanish.
Spain in part has based its arguments on UN Law of the Sea -- a treaty that Colombia never signed.
US-based company Sea Search Armada, whose subsidiary claimed in the early 1980s that it had found the galleon, was engaged in a long-running ownership battle with the Colombian government.
The find however was not confirmed, and in 2011 a US court ruled that the wreck was Colombian property.
A team of Colombian and foreign researchers, including a veteran of the group that discovered the wreck of the Titanic in 1985, studied winds and currents of the Caribbean 307 years ago and delved into colonial archives in Spain and Colombia searching for clues.
The San Jose has long been the source of fascination and popular legends, and even figures in Gabriel Garcia Marquez's novel "Love in the Time of Cholera."