Great question!
All literature that escapes the dawn of time becomes timeless. The Bible is timeless. But the stories it tells are thousands of years old.
But going straight to the point, people like stories, I’d say one of the requisites is having good storytelling. Another requisite is the subject. Books that debate the great questions of humanity, human nature, or more philosophical matters, are good candidates for timelessness. Some examples: stories about good and evil (The Lord of the Rings), love (Anna Karénina), change (One-Hundred Years of Solitude), moral options (Crime and Punishment), obsession (Moby Dick), etc.
Another perspective of timelessness: a story that travels through time. Repeating the cycle: birth, life, death through multiple generations. Gabriel García Márquez wrote timeless stories. Stories with epic reports are also good candidates: Homer’s Odyssey, Os Lusíadas by Luís Vaz de Camões, Foundation books by Isaac Asimov.
And yet another perspective, seminal books that somehow founded or marked a specific moment in history, style, or literary form. Dostoievski’s psychiatric romances, the magical realism of One-Hundred Years of Solitude, the fantasy of The Lord of the Rings, the narrative style of José Saramago.
Finally, there are timeless and premonitory stories. 1984 and Brave New World belong to this category. If the world is made up of cycles, these books will never be out of their time. I think I’ve exhausted my perspective of timelessness.