In an interview with IGN, Motomu Toriyama, Director of the Final Fantasy XIII trilogy, discussed how XV may be linked to XIII.

He was asked about Etro – the goddess in Final Fantasy XIII-2 – making an appearence in the debut trailer for Final Fantasy XV, and replied with the following:

You must remember, it was a long time ago that we named those three games: XIII, as well as Versus and Agito which we now call Type-0. Obviously those three projects were going to be developed against the backdrop of this Crystal trilogy, or Fabula Nova Crystallis. But each project has a different set of characters and they’re set in different universes and worlds.

When Etro is mentioned in the context of XIII and XV, we’re referring to the same goddess of Death. It’s the same goddess, but how she’s featured, how she appears and how she’s involved with the story is completely different. They’re different stories and different projects. So while it’s the same character, her involvement is very different.

He also discussed Lighting’s story arch and if it was coming to an end or stretching into XV’s.

The Final Fantasy XIII trilogy is definitely coming to an end; that’s definitive. Lightning’s saga is coming to an end as well, so all the worlds and areas like Cocoon and Gran Pulse surrounding her tale will be done with too. Having said that, there is a possibility that they may be used or depicted in a future project, but not a whole game.

There won’t be another full Final Fantasy title looking at Lightning or these areas.

It seems like he is suggesting some bare references will crossover into XV but nothing substantial; nothing in the form of playable characters or familiar worlds.