The Costa Concordia was on a trip around the Mediterranean when it hit a reef near the Isola del Giglio late Friday.
Eight people were killed and several people were still missing after jumping overboard in panic as the ship began to tilt, the Messaggero newspaper said.
One of the victims was a man in his 70s who died of a heart attack caused by the shock to his system when he jumped into the icy waters, reports said.
Over thirty people were also injured in the accident, several seriously.
Most of the 3,200 passengers and 1,000 crew members were quickly evacuated, but coast guards struggled to rescue around 200 people stuck on board.
Helicopters with spotlights were used to help rescuers.