A new next-gen Superman game is reportedly in development, presumably for PS5, Xbox Series X, and PC.
Unfortunately, further details beyond this are currently very scarce, but it's noted that before this game releases, Warner Bros. Interactive Entertainment will release Warner Bros. Montreal's new Batman game first, followed by Rocksteady's new DC Comics game, which is rumored to be a Justice League game. The report comes way of The GWW, which cites numerous sources that aren't identified for obvious reasons.
The report makes no mention of what developer is working on the game, but makes sure to note it's not Rocksteady. Within the Warner Bros. Interactive Entertainment umbrella is a lot of studios who could be working on the game. Beyond Rocksteady, we can probably remove NetherRealm Studios, Monolith Productions, Portkey Games, TT Games, WB Games New York, WB Games San Diego, WB Games Boston, and WB Games San Francisco off the the potential developer list given either their past history or based on what we already know they are working on.
Montreal or Avalanche Software or an outside studio. More likely than not, it's probably not the latter two, which seems to suggest this could be a second project at Warner Bros. Montreal, which is known to have multiple teams.
Of course, all of this should be taken with a grain of salt, like any unofficial report. If this game is indeed in development, it's probably early in development, so things can change. Further, how many years did we hear that Rocksteady was working on a Superman game? Even if it was at one point, we never got to see this game.