Fascinating question. One possibility is that Montresor is on his death bed and wishes to confess all of his sins in order to be absolved, which would make his audience a priest. After all, confessions to a priest are protected. They have "confessional privilege." Mostresor begins his narrative by pointing out how often Fortunato had "injured" him and had even moved to insults, as though he is attempting to justify his murder. Additionally, Montresor's explanation of his coat of arms and his family motto (which amounts to "No one hurts me and gets away with it") served as warnings to the doomed man, but Fortunato did not listen.
Another possibility is that Montresor's audience here is his child or grandchild--someone who will inherit his family home, completely with the catacombs and the fifty-years entombed man. This could explain some of the bragging tone of the narrative, as though Montresor isn't ashamed at all and may even expect his ancestors--who, after all, share his coat of arms and family motto--to do something similar, should the occasion rise.