Apparently Doom 4 was added to Steam beta subscription database, according to PC GamesN. The Steam database entry which is probably Doom4 is here:
This could mean that the game is being probably tested on Steam. There are speculations that game could be close to being released. But how long that means is a question. Beta testing phase has no time limits and probably there would be some trailer few months before the release, which still did not happen. Also as Id Software just finished work on additional Doom 3 BFG levels and moved over programmers from their mobile game division (and effectively closing it) it rather sounds like they could spend another 6 months or maybe more on finishing all work, optimizing, fixing bugs, adding features based on feedback from beta testers and so on.