Between this announcement and the report on McKay helming a Nightwing film in the DCEU, I'm starting to question the reports on The Batman apparently being based on Arkham Asylum and the use of Deathstroke as one of the main villains.
Not saying that those reports aren't valid, but between getting someone like Reeves to direct the film, announcing a Nightwing film and the several references to the death of Jason Todd in BvS and SS, it all feels like the natural path for Warner Bros to go in here is to use Under the Red Hood as the primary source material of The Batman's plot.
UtRH has that sort of personal and emotionally complex narrative that would fit a director like Reeves (i.e. Cesar and Koba's friendship/rivalry in DotPotA), it's a natural way to capitalize on the veteran Batman angle they're going with by having Affleck in the role and it'd connect the previous references to what happened to the second Robin while also allowing a possible introduction to the original Robin and his own path to becoming Nightwing (setting up the Nightwing solo film).
Then again, I suppose it could be possible that Under the Red Hood is already a part of the existing plot for The Batman and it just so happens to be set inside Arkham Asylum and feature Deathstroke for some reason.