Homer didn't have a comprehensive word for mind. the psyche and the conscious self had not yet been combined. He understood events as repetition of the past, and individual consciousness was not a part of that. But early Greek thought played a role in the complicate history of the concept of the soul.1
By the time of Plato these ideas had taken shape. The Phaedo and Timaeus are works which demonstrate the consious separation of the knower from the known and the dual nature of the body and the soul. Modern thought was possible: the complicated history of the concept of the soul. Whoa!
Pythagoras and Orphic doctrines all came into play, because Plato was a mystic in his own Platonic way. The pre-Socratic Naturalists saw things in terms of "stuff". But Plato's metaphysics showed that this was not enough. This is the incredible complicated history of the concept of the soul. Rock and roll.2
1 For an interesting discussion, see E.R Dodds, The Greeks and the Irrational, Berkeley, 1953, pp. 45-150.