No, the upcoming Superman film Man of Steel cannot exist in the Batman universe of the Nolan films.
The entire point of what Nolan wanted to do was posit Batman in a world without any superheroes, without even superhero comic books existing, and where everything tries to be grounded in realism as much as possible.
And crucially, that world in the Batman films was meant to be brought to an end, to close it off so that it isn't in any danger of having the underlying premises and themes undermined and erased by shoehorning in flying aliens who shoot lasers from their eyes while fighting monsters in outer space.
Picture Batman battling the Joker in The Dark Knight for a moment. Think about that Gotham City and Batman's struggle with moral dilemmas and the questions of symbolism as a means of transcending the reality of our mortal selves. Think about Batman's struggle to overcome the contradictions inherent in his own vigilantism versus his goal of restoring the rule of law. Think about how he fights the drug dealing mobsters and gets mauled by the dog. How he feels himself becoming ineffective against organized crime because they no longer fear him due to his rules. How he spends days trying to find the Joker and then battles his way through a building for the final showdown, only to come face to face with an impossible situation involving a friend and ally whose emotional and physical pain has turned him into an agent of evil, where Batman must risk his own life to save a kidnapped boy from being shot.
Then imagine that Batman goes off to punch alien monsters in space with help from his flying laser-eyed alien friend and magic goddess empowered by Zeus.
Christopher Nolan has made it clear that he ended the "Nolanverse" for Batman. So that bat-world won't be part of the new DC Comics film universe full of other superheroes. Instead, yes Man of Steel will be the first in a new line of films that leads to a Justice League movie starring the new Superman from the rebooted franchise, plus a brand new rebooted Batman, and several other superheroes. It's possible that the studio might've gone in and shoehorned a cameo by someone like Bruce Wayne/Batman into Man of Steel as well, but that's not confirmed and is just a rumor created because of misunderstanding about Nolan's response to a series of questions that included some things he just can't remark about one way or another.
The point is, no the new Superman film cannot exist in the Nolan Batman universe. But it CAN and WILL exist in a new universe that includes a new Batman and other superheroes, including the Justice League.More questions on Man of Steel (2013 movie):