A domain registration points toward the Final Fantasy X-2 treatment for Final Fantasy XIII.
In the PS2 era, Square Enix didn't want to let the popularity of Final Fantasy X dissipate without capitalizing on it a second time, so it created a direct sequel called Final Fantasy X-2 that starred many of the same characters. If a new domain registration means anything, Final Fantasy XIII could be in for the same treatment.
Supererogatory caught a domain registration for "FinalFantasy13-2game.com" made by Corporation Service Company. This might seem like someone else trying to get in on Square's business, but CSC is an official Square Enix registrant and has filed for many other domains in the past.
Square Enix uses "FinalFantasy13game.com" as its website for Final Fantasy XIII, so "FinalFantasy13-2game.com" is likely what it'd use for the direct sequel's website. The company has an event planned for January 18, 2011 called the Square Enix 1st Production Department Premiere, where the "1st Production Department" that worked on titles like Final Fantasy XIII will presumably be revealing something, or finally going over more details on the long awaited Final Fantasy Versus XIII for PlayStation 3 and Final Fantasy Agito XIII for PSP. The event would also be a good place to announce a title like Final Fantasy XIII-2.
If Final Fantasy XIII-2 is swimming around over at Square Enix, I'm wondering if the company would handle it the same way as X-2 or if it'd be more of an extension of XIII. Final Fantasy X-2 added new aspects of gameplay, such as a costume/job system, and allowed players to visit many different locations from the get-go in an airship. If the same were done for a XIII-2, it'd at least reduce any obligatory complaints about linearity.
Source: Supererogatory Twitter