Rumor has it that the next title for the Arkham series will be called Batman: Arkham Legacy.
Batman: Arkham Legacy is the rumored title
After several speculations of the next Arkham title like who the next villain was, this time around the new rumor revealed that the title will be called Arkham Legacy. This will be set after the Arkham Knight game, and reportedly the villain will be the guys from the Court of Owls.
A point of interest is the rumored title itself. There was a canceled Damian Wayne-starring game in the past. Some guys speculate that it would be loosely based from the Battle for the Cowl arc where the Bat-family members are fighting each other on who will take over the Batman mantle after his death.
WB Games has not made an official announcement yet, so all of these are just rumors and speculations from different sources. Nothing concrete yet.