Ports in Britain, China, France, Italy, Norway and Turkey have been invited to submit offers for the lucrative contract and the winning bid will be announced by the beginning of March, organisers said.
"We estimate it will take around two years" to scrap the ship, said Franco Porcellacchia, the engineer who has been co-ordinating the salvage on behalf of ship owner Costa Crociere, Europe's biggest cruise operator.
Porcellacchia said 19 large tanks or "sponsons" will be welded onto the ship starting in April. He explained these tanks would be gradually emptied of water to re-float the ship in an operation lasting up to 10 days.
The 290-metre (951-foot) ship, which crashed and keeled over off the Italian island of Giglio on January 13, 2012, was dragged upright in September 2013 in the biggest salvage operation on a passenger ship ever undertaken.
Salvage operators said the preferred option would be to tow the ship but they have also optioned the world's largest semi-submergible ship, the Dockwise Vanguard, in case it needs to be carried to its final destination.
"The project has been a great booster for the economy both locally and nationally," Costa Crociere said, citing a study that showed 60 percent of direct salvage costs, or around 261 million euros ($356 million), had gone to Italy.