Takashi Tokita, the director of Chrono Trigger, Parasite Eve, Final Fantasy IV, Live A Live, Final Fantasy Legends and other games tweeted out the following
— ????? (@Takashi_Tokita) April 7, 2017
When translated, what he wrote says
Top-secret mission begins !
Square Enix is a big supporter the Switch and wants to be one of the top publishers for the platform. Could this be a new IP?, or maybe a new entry in an existing series? Or could the rumors be true about a remake of a critically acclaimed classic now done for Nintendo Switch. It should also be noted that he worked on the various spinoffs of FFIV and the re-releases in addition to the main game. It is possible it is to do with that.
Whatever the game is, if it is just starting development now, then we probably wont see it at this E3, unless we are shown a very early teaser. Still it is exciting to thin what they may be working on.