Before J.J. Abrams was making Star Trek and Star Wars movies, he was developing a Superman movie for WB way back in the early 2000s called Superman Flyby. That movie never happened, but with Abrams' studio Bad Robot striking a big deal with Warner Bros, rumor has it that they want him to helm a Superman film.
This comes from The GWW's Thomas Polito:
If you don't know anything about Abrams' canceled Superman film, Mr. Sunday Movies has covered it here:
With Abrams being the one to invigorate franchises like Trek and Star Wars, I would love for him to take on Superman—particularly Henry Cavill's Superman. The franchise has been dead in the water ever since Justice League, and I think Abrams is a big enough director that the studio would be confident enough to push through if he made a Superman movie.
Though there are a lot of people who hate on Man of Steel and Batman v Superman, I think it ultimately boiled down to the writing. A lot of people loved Cavill's take on the Last Son of Krypton, and with Abrams' direction, we could actually get him in universally loved Superman film.
Of course, these are all just rumors for now. After The Rise of Skywalker, I'm sure Abrams would want to work on something that isn't a franchise film. Then again, we'll just have to wait and see for any official announcements.
Catch Abrams' Star Wars: The Rise of Skywalker in theaters Dec. 20.