The goddess to which Odysseus is most likely referring is Athena, the goddess of wisdom. She was the goddess to whom Odysseus prayed asking for success in his plan to escape the Cyclops.
Athena and Odysseus have a sort of a close relationship in the sense that, even though he is a mortal, Odysseus is admired by the goddess for his courage and intelligence. As Nestor tells Telemachus, he has "never seen the immortals show so much affection as Pallas (Athena) openly showed him (Odysseus)." (3. 251-252)
