The unreliable narrator's audience is never revealed in the short story. However, the narrator is desperately attempting to convince his audience that he is completely sane. Interestingly, the narrator mentions that he has the ability to hear "all things in the heaven and in the earth," as well as in hell, which is a clue that he is insane. The narrator also speaks confidently to his audience and is motivated to tell the entire story of how he murdered the old man in order to convince the audience of his sanity.
Given the fact that the narrator informs the police of his crime, one could assume that the narrator is telling his story from prison. He may be telling his story to a psychologist, another inmate, or a person interrogating him at the precinct. In my opinion, the unreliable narrator is speaking to a prosecutor in court and arguing that he was completely sane when he brutally murdered the old man. In this scenario, the narrator would be telling his story from a witness stand in court while addressing the prosecutor, judge, and jury.