In January 2012, 32 people died when a Costa Cruises ship ran aground off Tuscany, Italy.
Costa Cruises says it is looking into the claims, but stands by the statement it gave on Monday.
Costa Cruises is a subsidiary of Carnival and runs some of the company's total fleet of 100 ships.
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Costa Cruises said on Monday that the route deviation last Friday had been "unauthorised, unapproved and unknown to Costa".
The liner, owned by Genoa-based Costa Cruises, was carrying about 3, 200 passengers and 1, 000 crew members when it struck the rocks.
Capt Schettino, 52, has worked for Costa Cruises for 11 years, and the firm said he had passed all the required courses.
"Once returned to a floating state, the wreck will be towed to an Italian port, " Costa Cruises said in a news release.
Capt Schettino, 52, has worked for Costa Cruises for 11 years.
Costa Cruises boss Pier Luigi Foschi accused Capt Francesco Schettino of sailing too close to a nearby island in order to show the ship to locals.
In July Steiner launched its largest-ever oceangoing operation, the 25, 000-square-foot Asian-theme Samsara Spa, with a fitness center, on the Concordia, run by Costa Cruises, a division of Carnival.
Michael Thamm, now the president of Germany-based AIDA Cruises, has been appointed CEO of the Costa group, which includes Costa Cruises, AIDA Cruises and Spanish operator Ibero Cruises.
"The plan to re-float the hull in one piece gives top priority to minimising environmental impact, to protecting Giglio's economy and tourism industry, and to maximum safety of the work, " Costa Cruises said in a statement.
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Costa Cruises has been informed that today at 10:39, Italian time, a fire developed on board Costa Allegra in the engine room, the local electric generators located at the stern. procedures and the system of fire board were promptly activated and the special brigades of the board have occurred, the fire was extinguished and did not extend to any other area of the ship.
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Carnival had said in March that the sinking of its Costa Concordia cruises ship in January could wipe out profits this year as people shunned cruises.
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"For 2013, the company will capitalise on the increasing popularity of cruising in Asia with the deployment of a second Costa ship in China and the launch of a new Princess Cruises program for the Japanese market, " it said.
BBC: Carnival cruise operator sees profits beat expectations
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