If it fell to the seabed, a depth of more than 230 feet, salvage operations would become much more difficult and the fuel tanks could be ruptured, sending 500,000 gallons of diesel and heavy oil into the waters off the Tuscan island of Giglio, The Daily Telegraph of Britain reported.
Movement of the ship is being measured hourly with sophisticated instruments attached to the hull.
"The more time passes, the weaker the wreck [of the Concordia] becomes," said Alessandro Gianni, director of Greenpeace Italy. "The best option would be to remove it in its entirety from Giglio, even if that takes a couple of months longer."
Trying to cut the ship into pieces in the water would be "disastrous" for the environment, he said.
When the cargo ship Rena broke up off the coast of New Zealand this year, pollution affected about 40 miles of coastline, Greenpeace Italy said.
There's no immediate danger of the 950-foot Concordia breaking up or sinking deeper into the sea, experts said.
But if its rate of movement increases, it will become more unstable.
The death toll in the Concordia wreck is 17 but 15 people remained unaccounted for and are presumed dead. The ship had been carrying 4,200 passengers and crew.