In Coelho's The Alchemist, the author does not specifically state when the story takes place. In fact, the book could take place at any time, for there are no references to technology (telegraph, telephone or computer) or even world events that would allow the reader to pinpoint a particular time in the history of the world. And it would seem that this make perfect sense in light of the book's purpose: Coelho responds to a personal, spiritual awakening that he experienced—as written in his novel, The Pilgrimage. In The Alchemist he continues to share insights that he garnered from that experience. His messages are timeless ones that are important to hear regardless of the time period in which the story might have taken place.
To me, one of Coelho's messages is that everything comes from the Soul of the World (God) and everything will return to it:
...everything has its Personal Legend, but one day that Personal Legend will be realized. So each thing has to transform itself into something better, and to acquire a new Personal Legend, until, someday, the Soul of the World becomes one thing only.
This also speaks to the constant state of change taking place in the world everyday.
This oneness with the universe is not a new concept by any means. The transcendentalists, for example, saw a clear connection between man and the natural world, and the great capacity for human beings to exercise wisdom beyond what might be expected from a mere man (or woman).
...transcendentalist literature also promotes the idea of nature as divine and the human soul as inherently wise.
Santiago learns to harmonize and understand nature, and he becomes wise beyond his years in paying attention to what the world can teach him.
Another important theme is that everyone has a purpose in the world even though many may never realize the truth of this:
No matter what he does, every person on earth plays a central role in the history of the world. And normally he doesn't know it.
Santiago learned a great deal from those who wished to help and advise him, as well as those who took advantage of him or disagreed with his quest or his methods.
Another important message is that love—true love—does not try to control the object of that love. The alchemist notes that Fatima, if she truly loves Santiago, will wait for him. She will understand that he must leave to pursue his Personal Legend, and in loving him sincerely, she will not try to stop or discourage him in any way:
Love never keeps a man from pursuing his personal legend. If he abandons that pursuit, it's because it wasn't true love.
Finally, Coelho asserts that there is only one power in the world. This power is the Soul of the World (God), and that this power can be found in every corner of the universe, but especially in that of love.
...everything under the sun is written by one hand only. It is the hand that evokes love...
The story is not set in a specific time period because the themes Coelho addresses in the novel do not belong to one specific era: these are timeless themes that have endured the rise and fall of powerful civilizations—but they remain unaltered.