Here when discussing the ethnic diversity of various intellectual notables
These are the times of the oldest wise men and philosophers among the Greeks. And that the most of them were barbarians by extraction, and were trained among barbarians, what need is there to say? Pythagoras is shown to have been either a Tuscan or a Tyrian. And Antisthenes was a Phrygian. And Orpheus was an Odrysian or a Thracian. The most, too, show Homer to have been an Egyptian. Thales was a Phœnician by birth, and was said to have consorted with the prophets of the Egyptians; as also Pythagoras did with the same persons, by whom he was circumcised, that he might enter the adytum and learn from the Egyptians the mystic philosophy. He held converse with the chief of the Chaldeans and the Magi; and he gave a hint of the church, now so called, in the common hall^1960 which he maintained.
It isn't unique! The birthplace of Homer was very contested throughout the whole of antiquity, and there are parallels.
A good ancient resource on this is a body of texts known as the "Lives" of Homer. A collection can be found in the Loeb edition Homeric hymns, Homeric apocrypha, Lives of Homer, ed. Martin L. West, 2004. Even that isn't complete -- it doesn't include things like the Clement passage you were looking at.
Life 6 in that collection, from Hesychius, has this to say on Homer's birthplace.
He is likewise indeterminate in respect of his homeland ... some said he was born a Smyrnaean, some a Chian, some a Colophonian, some a man of Ios, some a Cymaean, some from a place Kenchreai in the Troad, some a Lydian, some an Athenian, some an Egyptian, some an Ithacan, some a Cyprian, some a Cnossian, some a Salaminian, some a Mycenaean, some a Thessalian, some an Italian, some a Lucanian, some from Gryneia, some even a Roman, some a Rhodian.
Life 7, the "Vita Romana", includes some reasoning --
Aristodemus of Nysa argues him to be a Roman, from certain customs that occur only among the Romans: firstly from the game of pessoi [mentioned in Odyssey 1.107], and secondly from the practice of inferiors rising from their seats when superiors arrive [Iliad 1.533], customs which are still preserved among the Romans. But others have said he was an Egyptian, because he portrays heroes kissing one another, which is an Egyptian custom.
Also in Life 9, the "Vita Scorialensis II", one of the options for his birthplace is Egypt.
I doubt you're thinking of taking any of this seriously, but just in case you were ... don't. The "Vita Romana" gives a good idea of the kind of reasoning these ideas rely on. It's logical as far as it goes, but it's very selective and comes to a conclusion that's far more specific than the evidence warrants.
For the record, the earliest traditions we know of focus on Chios. This appears in the Hymn to Apollo, where the narrator acts in the persona of Homer ("a blind man") and tells his audience to report that the greatest poet is a man from Chios, and in Simonides, who quotes a line from the Iliad as follows (frag. eleg. 19.1-2 West^(2)) --
One thing the Chian man said, the very finest:
"Like the generation of leaves, so is the (generation) of men."
Don't take that too seriously either: people of the time did take it seriously, but it's all imaginary biographical traditions.
(Many of the tropes don't come from where these writers say they come from, anyway. The "Like the generation of leaves" trope appears in Near Eastern mythological/religious sources: Deutero-Isaiah 40.6-8, Sirach 14.18 (2nd cent. BCE, but definitely informed by Hebrew traditions rather than Greek). The "rising for superiors" trope that the "Vita Romana" mentions appears in much earlier sources: the Amarna version of Nergal and Ereshkigal, the Hittite Song of Ullikummi, and a parodic variant in Proto-Isaiah 14.9. The Iliad is much closer to the Nergal and Ullikummi appearances of the trope, too, as all three of them depict gods rising from their seats at the arrival of a superior divinity.)