Royal Caribbean has refused to comment on rumours that it is about to sign a deal to build a third Oasis-class ship.
The vessel would be a sister ship to the 5,400-passenger Oasis of the Seas and Allure of the Seas, the largest ships in the world.
The story has been reported by a Finnish newspaper, Turun Sanomat, which said that STX Finland's Turku shipyard, which built the two other Oasis-class ships, would also build the third ship, although the deal was pending financial support from the Finnish government.
There have been recent appeals to the government by trade unions involved in shipbuilding to keep Finnish shipyards competitive and secure new ship orders, said the newspaper, which also mentioned that the new Oasis-class ship would cost about $1.29 billion to build.
However, a Royal Caribbean spokesperson said the company was refusing to comment on the rumours.
Adam Goldstein, chief executive of Royal Caribbean, said back in 2010 that they had no plans to build a third Oasis-class ship.
He told CNN that although the vessels were "excellent performers", Royal Caribbean needed flexibility in its fleet, as the huge size of Oasis-class ships means they are limited in the number of ports they can call at.