There are numerous rumors spreading on the Internet regarding 'Tokyo Ghoul' Season 3 so there is a need to find out what's real and what's not.
What's Real: As of the moment, there is no direct announcement of a specific release date. The only basis for information is this statement from Gen Fukunaga, CEO and President of FUNimation Entertainment published in Game Samba:
"Ever since we began simulcasting the anime series last year, fans of the Tokyo Ghoul have been clamoring for a mobile game. With Season 2 now finished and Season 3 set for 2016, the anticipation for the mobile game has only grown higher."
The statement does not specify what is "set"-if it's a release date or production.
Anime News Network also attempted to gather more information but did not get any specifics.
"Funimation confirmed it is 'anticipating a 2016 release,' but the company did not specify whether it meant a release for the mobile game or the anime's third season. The company did not respond to ANN's requests for clarification as of press time."
What's not: As of this writing, reports mentioning specific dates are probably jumping the gun. There is no way to determine how far production has commenced (if at all).
Plot details and the news spreading that "the series will air during the Winter 2016 anime season, and Madhouse will be taking over the animation from Studio Pierrot" quoted in various sites and referring to AnimeMaru as the source (which claimed it was "confirmed") are probably not true as Anime Maru is a satire site.
According to Anime Maru's About Us page:
"Anime Maru is a regularly-updating online publication that is dedicated to bringing you up-to-date news and commentary about the anime industry."
However, they quickly add:
"Ok, for liability reasons, I have to come clean. Anime Maru is a a satirical publication. Nothing on this site should be interpreted as factual nor as a claim to fact."
Finally: "In conclusion, Anime Maru is fake anime news."