While the exact dialect of Ancient Greek spoken by Odysseus is not specified in Homer's Odyssey, we can assume it would be a form of Mycenaean Greek, the language spoken in mainland Greece during the Mycenaean period (c. 1600-1100 BC). This is based on the fact that the Odyssey is set during this period, and the language reflects the pronunciation and vocabulary of that time.
However, it's important to note that the Cyclops, being a mythical creature, is not portrayed as speaking any recognizable human language.