Yes, Sony has just announced that, by way of a deal with Activision, it's bringing Crash Bandicoot to PS4. One catch though. It's not a new game. It's full remasters of the first three games in the series. Crash Bandicoot, Crash Bandicoot 2: Cortex Strikes Back, and Crash Bandicoot: Warped are all heading to current-gen, though the exact nature of the remakes currently isn't clear.
That said, coming all the way from PS1, I wouldn't at all be surprised by full rebuilds. Those games of three generations past are not going to look great with just a quick upscale.
There is (sort of) a new version of Mr. Bandicoot on the way though, in the form of an appearance in Skylanders: Imaginators in October. It’s worth noting that we were told that this would be Crash's first PS4 appearance, so don't go expecting those remakes until a way into 2017 at least.