Context matters for this one. As the earlier poster said, "sleepyhead" is the most literal single term for what you ask. But it has usage restrictions. It's typically used as a form of address; that is, it's more natural to CALL someone "sleepyhead" directly than to refer to someone AS a sleepyhead.
And, as mentioned, it carries a silly or childish connotation. You would never say to your boss, "Lets not hire him, he's a sleepyhead."
Some adjectives you might use to describe a sleepy person: Lethargic, dopey, narcoleptic, fatigued.
A friend of mine, when he's sick or un-rested, will say, "I'm really dragging ass today." This sounds completely natural to a native English speaker's ear, but is highly vernacular.