Square Enix will announce news about the future of Final Fantasy XIII on September 1, Andriasang reports today
Presumably this will be a Final Fantasy XIII-3 that continues where Final Fantasy XIII-2 (and its DLC) left off, but Square Enix has not specified. They’ve only said more is coming, promising what’s called the “Final Fantasy XIII Lightning Saga: New Developments Presentation” on September 1 during an event in Shibuya, Japan.
https://kotaku.com/expect-more-final-fantasy-xiii-but-dont-expect-final-f-5923638
Rest assured there probably won’t be news of Final Fantasy Versus XIII
https://kotaku.com/rumor-final-fantasy-versus-xiii-is-dead-update-5927645
Future Final Fantasy XIII Developments To Be Announced on Sept. 1 [Andriasang]