The usually accurate insider Shinobi602 has revealed a ton of things in the past, most recently the Skyrim remaster, and now he claims that Sony will announce God of War 4 during E3. Shinobi602 also says Kratos is in the game, but might not be the protagonist.
He is not sure about the name either, so God of War 4 might be called something else. Finally he also says that we won't get to see anything from The Last of Us 2 on Sony's press conference.
Sony's presser starts in the wee small hours of the monring, and then we'll get to know if Shinobi602 was right. You will be able to see it here on Gamereactor.