This is such an interesting question, especially considering that Marquez's stories usually contain an indeterminate time and place. A Very Old Man with Enormous Wings is no exception. This is because Marquez uses a technique often referred to as "magical realism" which simply means that elements of magic and fairy tales are embedded within the same story as elements from our reality. This usually creates an intense frustration for the reader who is unable to determine any type of moral to the story. Likewise, this leads to the mood of confusion and frustration, even within the characters of the story.
A Very Old Man with Enormous Wings contains characters with names that suggest a Spanish-speaking country, although no country is ever named. In addition, we are told of times past and seem to be in the midst of a fairy tale world, but are given references to modern methods of transportation which seem to pinpoint the story to the twentieth century or later. By not setting the story in a particular time or place, Marquez creates a timeless effect which nicely leads the reader to consider his story to be universal.