The story is published under the name of Edgar Allan Poe. This suggests to me that Poe is representing it as a translation of an old manuscript which was found among the papers of Montresor after his death or among the papers of the person to whom it was sent. Montresor might have written it as a letter one night when he was drunk and then decided not to send it the next morning. Poe did something similar with his story titled "Manuscript Found in a Bottle." I don't see how Montresor could be narrating the incident to anyone in person and then how Edgar Allan Poe got hold of it. That would spoil the verisimilitude Poe was trying to achieve. If Montresor was supposedly confessing to a priest, he should have sounded more contrite. Instead he seems proud of his accomplishment. As I see it, the manuscript would have been written in Italian, or French, or possibly even in Latin, and then translated into English by Poe, who knew nothing about it except what was in the letter.
What was Montresor's reason for confiding his crime after fifty years? He probably kept his secret completely to himself for all that time and then, when he felt completely safe, confided in the person he addresses as "You, who so well know the nature of my soul" because it is human nature to wish to confide secrets to someone. But Montresor seems to have been a heavy drinker, and it is also human nature to reveal secrets when we have been drinking. (In vino veritas.) Montresor may have written the letter late one night was he was feeling lonely and then never sent it because he was still playing it safe. If he hadn't confided in "You, who so well know the nature of my soul" in fifty years, why should he trust even that person now? If he didn't send the letter immediately, he could have kept it, thinking he might send it later. And then he might have forgotten about it. He must have been quite old when he wrote it. If he was forty when he committed the crime, he would have been ninety when he wrote about it. He might have been dying--and died before he could either send or destroy what he had written.
I can't see Montresor confessing to a priest, because he does not seem like the sort of man who would go to church and confess his sins to priests. If he is worried about being punished in the afterlife, there isn't any indication of that in the story. He doesn't sound like a man who is ashamed of what he has done to Fortunato. Rather, he seems proud of having committed the perfect crime and having fooled everyone. He wanted the perfect revenge, and he got the perfect revenge. He achieved "closure."
If he is confessing to a priest, shouldn't he be confessing in Italian? Or Latin? Is Poe supposedly eavesdropping and translating the confession into English as it goes along? The narrative we read in English has got to be a translation from another language in order to preserve the fiction. Either Poe overheard the confession or found the original manuscript. In any case, a confession to a priest would not include so many fine details, such as Fortunato's prolonged coughing, for example.
No one really knows who Montresor is talking to in the story. We can only guess. I think he is talking to a priest. Montresor is obviously confessing his crime of so many years ago, and it appears that this is not the first time he is confessing the same thing. He is retelling, with some delight, the details of his murder of Fortunato. He goes into deep details about the crime. Montresor never gives a specific reason for the killing, just that he had taken all he could of Fortuanto.
"The thousand injuries of Fortunato I had borne as best I could, but when he ventured upon insult, I vowed revenge. You, who so well know the nature of my soul, will not suppose, however, that I gave utterance to a threat."
In this quote, whomever Montresor is confessing to, knows him very well. When he states that this person knows the nature of his soul, makes one think he is confessing to a priest. When a person goes to confession, they know that whatever is said there, will stay there. We can only assume that he has confessed this type of crime before, and that is why the person knows his soul so well.
Poe was the master of suspense. He created stories and characters that kept us guessing. He was so clever in the way that he weaved all of our senses into the stories. By leaving us guessing who Montresor is talking to, is just another way Poe makes us think of human nature. He makes us look at the core of who each of us truly are.
MyGuess is that he is talking to a priest