Looks like it's in development, although like INFINITE will probably take a while to come out.

It's unclear whether it's a reboot or will somehow continue the story. Although INFINITE initially seemed to be a seperate thing with a similar theme, the DLC Burial At Sea connected it as a prequel, explaining that a good chunk of Rapture's tech came from a cross-dimensional information exchange with Columbia.


Rapture seemed to be totally destroyed in the second game, but the "canon" of that is debated since Levine was not involved and it's contradicted a bit by the other games.