Movements were registered overnight by onboard sensors. It was unclear if they were just vibrations as the ship settles or if it's slipping off the rocks.
The Costa Concordia was carrying more than 4,200 passengers and crew when it hit rocks off the island of Giglio last Friday. The captain made an unauthorized diversion from his programmed route. Eleven people are confirmed dead.
Any significant shift of the ship could be dangerous for divers trying to locate the more than 20 people still missing.
There were also fears that movement could damage tanks holding 500,000 gallons of fuel oil.
Capt. Francesco Schettino remains under house arrest, facing possible charges of manslaughter, causing a shipwreck and abandoning his ship.