According to media reports citing coast guard officials, divers found the bodies near a restaurant where passengers were dining when the ship hit rocks near the Tuscan island of Giglio late Friday night.
The BBC said the bodies were taken to shore for identification.
According to the Associated Press, the discovery reduced to 15 the number of people still missing.
On Saturday, officials confirmed two French passengers and a Peruvian crew member had died. Costa Crociere has stated that 3,200 passengers and about 1,000 crew were evacuated.