We are actually told very little about the audience of Montresor's story. However, if we think about the story and the way that he is commenting upon a deed that he committed over fifty years ago, as the ending of the story makes clear, perhaps we can surmise that this story is something of a deathbed confession. Note what we are told of Montresor's audience in the first paragraph:
You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat.
The audience therefore knows Montresor intimately and profoundly, having knowledge even of "the nature of [his] soul." Perhaps we can speculate that Montresor, coming to the end of his life, feels the need to share his one terrible secret before he dies, and that he is sharing it with his family priest, who already knows Montresor through and through because of the sins he has revealed through confession. The declarative nature of the story would lend itself to this kind of conclusion.
This story appears to be written as a letter which Poe somehow finds and translates into English and publishes in a ladies' magazine. The original letter may have been in Italian or it might have even been in French, since Montresor is a French name. Montresor wrote the letter fifty years after walling Fortunato and leaving him to die. However, the letter that falls into Poe's hands might be much older than fifty years. Montresor obviously did a lot of drinking. (In fact, his guilt feelings after the crime may have motivated him to drink even more heavily.) There is a good possibility that he wrote his confession one night while intoxicated and decided against sending it when he thought about it while sober the next day. The letter might have been found among Montresor's papers after his death, or it might have even ended up in some museum's archives. There is also a good possibility that the confidant or confidante to whom the letter was intended never saw it but that Poe and his readers are the first to learn about Montresor's terrible crime. The whole business of the written confession to a trusted friend is just a literary device which enabed Poe to describe how a man could commit a horrible murder without ever getting caught and punished.