If you want to get hands-on with Rockstar's next helping of GTA, then you'll need to invest in some new hardware. According to Pastebin's post, GTA 6 is just too big for the PS4 or Xbox One, but if most in the gaming world were being honest with themselves, nobody was expecting Rockstar to release the next GTA on current systems anyway.
This does mean that, aside from the touched-up GTA 5 release, there hasn't been a Grand Theft Auto game on current-gen. Not an exclusive one, at least.
The Pastebin user's exact wording was, "This game cant come out for PS4 because of memory restrictions". There's more on why later, but for now just brace yourself to drop some cash on the next series of consoles released by Sony and Microsoft. The PS5 (or whatever Sony end up calling it) is expected somewhere between 2020-2022, with some touting 2020 as being the most likely launch date.
That'd mean GTA 6 is coming out two years after Red Dead 2's release in late-2018. That almost fits the prior release gap between the first Red Dead (2010) and GTA 5 (2013).