The original rumor started with the Polygon.com, which cites confirmation from multiple sources that the game will not have a singleplayer campaign, on any platform. According to those same sources, the singleplayer mode was canned as there just wasn't enough time to get it done before the official release date, set for October 12.
It appears that Treyarch studio will focus on the multiplayer part of the game, the popular Zombies mode and even some other co-op multiplayer modes while the Charlieintel.com site launched another rumor suggesting that Raven Software, a studio which was working on most Call Of Duty titles, will focus on making a battle royal mode.
Earlier rumors suggested that Activision was already aware of the battle royale popularity so we would not be surprised if it wants to take advantage of it by designing a similar mode for Black Ops 4.
As announced by Activision earlier, there is a big Call of Duty: Black Ops 4 reveal scheduled for May 17, and the game is set to launch on October 12th on PC, Xbox One and Playstation 4.