Halo Infinite, which as far as we know is also Halo 6, was teased in June at E3 and, more importantly, confirmed for PC. We don't know much about it, but thanks to a recent 343 Social Stream on Mixer, we do know that it probably won't have a battle royale mode.
"I'll tell you right now, the only 'BR' we're really interested in is 'Battle Rifle'," 343 Industries lead writer Jeff Easterling says in response to a question about the mode's possible inclusion. "The original 'BR.' So, calm yourself."
(The comment comes at the 55m55s mark. If you can't see the time on the bar because Mixer is terrible to embed, it's right after the bit where they're talking about the white BMW.)
That's obviously not an all-caps "NO" laser-etched into titanium and mounted atop Grand Teton for all the world to see, but it's enough of a dismissal to be worth taking seriously, particularly given the popularity of the mode and the fact that virtually every other shooter of note is embracing it. Activision and EA have both made a point of emphasizing the presence of battle royale modes in Call of Duty: Black Ops 4 and Battlefield 5. But it's possible that 343 and Microsoft are banking on burnout by the time Halo Infinite comes around, or perhaps that it can stand out from the crowd more effectively at this point by not running with it.
Of course, there's always the possibility that minds will change and we'll be hearing about Halo Royale at the next E3. There may actually be time for that: A release date hasn't been set but we've put our money on it showing up sometime near the end of 2019.