Just about every analysis I have read for this refers to it as 3rd-person omniscient, but there is one that is really interesting.
Scroll down to the RTF link: Subject *AP English class SB...
In “A Very Old Man with Enormous Wings,” García Márquez makes use of several highly inventive diversions from the basic story line to make interpretation even more elusive. In these narrative diversions theme and technique become inseparably intertwined. Although the old man/angel is central to the story, and every event bears on him, his appearance, behavior, identity, fate, or effects, the attention focused on the old man is frequently interrupted by shifts of focus to other characters, who are sometimes named and described at length. The obtrusiveness of the narrator, who is both at one with and apart from the other characters, also functions to distract the reader. The story, in fact, vacillates between the perspective of the omniscient narrator and that of the villagers, individually and collectively. When Father Gonzaga enters, for example, he reveals his suspicions about the old man, his observations about him, his sermon to the assembly of villagers, and his promise to seek advice from higher authorities. A few pages later, there appears a synopsis of his correspondence to the pope about the old man, and after another few pages, the waning of the old man’s popularity seemingly cures Father Gonzaga of his insomnia. Then the old man disappears from the narrative altogether.