Actually, these rumblings aren't entirely recent. There's been some talk that seemed to reinforce the idea, but in reality there has been talk almost since Man of Steel that Superman himself could die in the second installment, and be resurrected later.
I don't think so, and we'll get into why below, but first let's roll the notion around a little bit and see why it is that people are so convinced, and what evidence is being presented by reporters, Redditors and others who believe there's another monument ready to be built before the Justice League can come together.
First off: while there has been quite a bit of talk online about why this would be a foolhardy idea, pointing that out would only cause the comments thread below to fill up with jokesters pointing out that's never deterred Hollywood before. So let's anticipate the "it would be stupid to do that," "yes, but DC is stupid" arguments and assume for the sake of argument we can do without them.
The arguments for killing a major character in the film are actually pretty straightforward.
- Warner Bros. has always wanted to do a Death of Superman movie.
Since the graphic novel remains one of DC's all-time bestsellers, it makes sense in terms of market awareness. More people have read The Death of Superman than almost any other DC Comic published in the modern age.
The famous Kevin Smith script Superman Lives, which you can find online, even adapted the storyline to the best of what they thought they could in the context of a single, stand-alone movie.
- There were Doomsday/Bertron Easter eggs on the Man of Steel Blu-ray.
"Beware Bertron's curse, for he is named Doomsday," says a message hidden in one of the featurettes on Man of Steel's Blu-ray.
Bertron was a Kryptonian scientist who lived hundreds of years ago. Fixated on creating the "perfect" life form, he evolved something he thought could bear the ravages of the planet's most unforgiving landscape, and then set the cloned infant free there to be devoured by the elements and local animal life. Scraping up the leftover genetic material, Bertron did this hundreds of times, essentially forcing the clone to rapidly evolve.
Ultimately, the being that was created was virtually indestructible and had evolved the ability to resurrect itself after death, having "evolved" past whatever killed it so that it couldn't die the same way twice. Bertron had succeeded in making an immortal and powerful being--but that being was barbaric and impossible to control--and it carried with it the genetic memory of generations of abuse, driving it to destroy Bertron and basically anything else that crossed its path.
Eventually subdued and bound, the being known as Doomsday was fired off into space--where its cell crash-landed in what would later become Ohio and was buried deep underground, where Doomsday "hibernated" for decades or centuries before he woke up and tore through the East Coast of the United States, stopped only when Superman sacrificed his life to destroy the beast.
- We don't yet know who the villain is...
Will Batman and Superman square off? Yes.
Will they come to blows in some form or another? They pretty much have to, to justify the title.
But Batman won't be the film's big bad. That would be madness. With Lex in the wings and dozens of rumors as to what villains might play a role beyond him, it's clear we won't be dealing with just a meet-fight-team-up story; they'll have to do something together when they team up.
Doomsday, meanwhile, is likely to be a fully-CG character and so you could keep him under wraps pretty easily, relative to something or someone that you'd have to be on set to shoot.
All that said...
Even with those answers in place, if there's going to be a death, it's pretty unlikely it will be Superman.
Henry Cavill, Ben Affleck and Amy Adams were the only actors whose names were mentioned specifically on the press release announcing Justice League when Warner Bros. told investors about their slate.
Kahina the Seer, a member of The Others and supporting player to Aquaman, might be a solid candidate; in the upcoming, animated feature Justice League: Throne of Atlantis, Aquaman ends up joining the League after coming to avenge the death of an Atlantean. Could we see something similar here? It's not out of the question, and while Kahina could be an interesting addition, it would be odd to see her get a big role since she died before Aquaman and the Others launched as a comic book title, meaning that she has a relatively small footprint on DC's history even in the context of the New 52.
Nevertheless, we've seen dressing rooms with her name and that of KGBeast, a character appearing currently in Aquaman and the Others, on the set of Batman v Superman.
...Of course, those names could also be fakes used to throw off fans and set spies. And who's writing Aquaman and the Others right now?
...Doomsday creator Dan Jurgens, of course.