I believe that Poe is presenting this story as a translation of an old letter that somehow came into his possession. Montresor would have been around forty years old when he committed his crime, so he would have been around ninety when he wrote the letter to the person he calls "You, who so well know the nature of my soul." He must be dead by the time Poe receives the manuscript. It was written in either French or Italian and was found among the papers of the recipient after his death. Either that, or Montresor wrote the letter one night while he was drunk but never sent it, for obvious reasons, so it would have been found among his own papers after his death. Although the letter was written fifty years after the crime, it could have taken another ten or twenty years before it somehow found its way into the possession of an American editor who translated it into English. The point is made that fifty years passed before Montresor decided to reveal his secret. This would only be to provide positive assurance that the murder had been perfectly successful. If no one has found the body in fifty years, then no one is ever going to find it. And even if someone did accidentally find Fortunato's skeleton, there would be no way to identify it, and no one would try to solve a fifty-year-old murder. Even if it were possible to solve the murder, Montresor would be dead and out of reach. We readers all know that Montresor was guilty of a horrible murder--but so what? We could even tell the authorities where to find the body--but so what? Montresor must be dead. He is probably one of those many skeletons he describes in the catacombs.
I believe this story must be regarded as having been in writing and that it is not dialogue being overheard by a priest or someone else. A priest would ask questions. If Montresor were speaking to someone (other than Fortunato) there would have to be some slight clue that this was the case. An oral confession would not contain so many specific details.
A fine question.
Three possibilities come to mind.
First, no one, or rather, himself. I see him running over and over the story in his mind like a favorite vintage.
Second, God. I see him as so proud that he'd brag of his sins even to God at death.
Third, a new victim that he wants to scare in his old age.
This is a good question for the discussion board.
I certainly do not believe Montresor is sharing his story because he feels guilt and/or remorse. I personally could picture Montresor relaxing with some friends in a smoking room LOL with a cigar lit and he suddenly decides to tell this story...not sure for what reason, however. He is smug enough that he could be telling it because he is quite proud of his plan that worked so well!
I personally think that montresor is on his death bed and is confessing his sins to a priest that he gets to see before he dies. I think this because the story is being told 50 years after it happened and if you think of the age he must have been when he did the incident then he must be very old and almost dying.
I believe the two previous answers are too limited in scope. First, Poe built a work that holds up when on every level that language operates. Second, since Montressor is unreliable, he may have felt guilt for his crime, but attempts to cover it: "My heart grew sick -- from the dampness . . . " comes to mind. Poe leaves the question of guilt open to us. If Montresor fails to possess humanity, he is simply a monster; I do not believe Poe wrote such tales. His characters feel the guilt of their crimes. Montresor,too, feels guilt, but tries to cover it with his bricks, literally and figuratively. Of course, he fails to keep it concealed, because he is now revealing it!
He may be talking to God, or the reader, or to himself. Perhaps it is addressed to his contemporaries, many of whom failed to recognize or believe Poe's ability to purposefully compose a story with such mathematical-artistic precision that it holds up on every level possible -- like Shakespeare's work. Poe was a genius. The perfection of this story cannot be ignored. It contains perfect solutions in every dimension language operates, which, no offense, the previous two posts failed to even allude to.