According to a blog post on the European Square Enix Members website, Final Fantasy XIII-2 will be receiving a demo very soon.
On January 10, a demo for the game will be hitting the PlayStation Network in North America. The following day, the same demo will be arriving on the PSN in Europe and Xbox Live internationally. While it wasn’t announced what would be included in the demo, it’s only a matter of days before that is discovered.
Final Fantasy XIII-2 was released in Japan for PlayStation 3 and Xbox 360 on December 15, 2011. The game will arrive on the same systems on January 31 in North America, and on February 3 in Europe.
Source: EU Square Enix Members Blog