Musician Trent Reznor has had a long relationship with game developer id. He scored Quake and did music for Doom 3 that did not make it into the game. No wonder there have been rumours about Reznor and Doom 4.
When asked about that rumour, Reznor replied, "I haven't been contacted by them and find it unlikely that I would have time at this point."
Reznor is currently busy with his new outfit How to Destroy Angels, which released its first EP this June. Don't rule out future Trent Reznor game involvement! Once upon a time, he even pitched a game concept that ultimately didn't get greenlit.