Because I am the only being in the universe, I believe you are not really a corporeal being independently posing this question. In fact, the universe is merely a construct of my mind so that I do not get bored or lonely. The screen on which I read the question, for example, is a figment of my imagination. You are a figment of my imagination.
More to the point, the you that I am imagining is not really you, but rather a fictional online persona that I imagine you created. I imagine a you that is only pretending to be you, so that you may write online questions that the real imaginary you wishes you could write. I imagine that you do this so that I may respond through the imaginary internet to the question, and explore the very real question of whether I am alone in the universe.
Now I am imagining that the imaginary you (the real imaginary you, not your imaginary online persona) is wondering if you are the only being in the universe. I image that you are wondering if I am just a figment of your imagination. I am alone in the universe, imagining that you imagine that you are alone in the universe, and that you are spending your time imagining someone telling you that you are merely part of his imagination.
Now, I cannot determine whether:
A) I am alone in the universe and you are merely imaginary.
B) I am dealing with the real imaginary you or with your imaginary persona instead.
C) I am merely a product of your imagination because you are alone in the universe.
D) I am merely imagining you because you imagine that I am imagining you.
If A, then yes, because it is definite that you are not real.
If B, then yes, because it is definite that you are not real, and additionally possible you are not really you.
If C, then no, it is not possible that you are not real. You are real, but I am not, so I am not really telling you whether or not you are real.
If D, then no, it is definite that you are real, but possible that you will believe A or B instead.
I really hope this answers your question, but I imagine that it will not.
Well, to an extent, I agree with Marcusmoon. Although the question itself seems a little futile. Since you're asking if it's possible that you are not real - well it's not really viable to say that it's impossible that you're not real. We could never command that degree of certainty to make that declaration. We would also have to breakdown about what you mean by "real", because there is no universal definition that seems to satisfy everyone. So my answer is also "yes" because it would be extremely difficult to refute or negate the "possibility" in your question.
Your existence can be proven by two ways: My point of view and Your own. From my point of view, i can state that only a mind can do reason. You do reason, therefore you are a mind, therefore you exist. From your point of view (now that i know you do exist) you can state that you think, therefore you exist, or you can prove that i exist, as i did to you, and then believe in my proof that you do exist.