* Endymion: This is the most likely candidate. Endymion was a beautiful shepherd who was granted eternal youth and sleep by the goddess Selene (the Moon). He sleeps eternally in a cave on Mount Latmos, visited by Selene every night.
* Epimetheus: This character was known for his "afterthought" nature, often acting without thinking through the consequences. He could be considered a "sleeper" in the sense of being oblivious to the danger of accepting Pandora's box, leading to the release of evil into the world.
* Hypnos: The Greek god of sleep, Hypnos could be considered "The Sleeper" in the sense that he represents the very essence of sleep.
It's important to note that "The Sleeper" isn't a specific character in Greek mythology, but a potential epithet for any of these figures.