I've been reading through a fraction of Ancient Greek literature, lately, and an odd thought occurred to me. In nearly every work of Greek literature that is tangentially related to sexuality (which, we've gotta admit, is quite nearly most of the well-known ones), sex is treated as universally desirable, and is a locus of control and power. Most of the discussion around women in Greek culture seems to revolve solely around sexuality.
As another example, Eros is often referred to as being one of those omnipresent entities in male interactions in Greek culture. The Symposium goes into some manner of detail on this point about Eros, describing maleness and sexuality as effectively identical concepts with no real distinguishing factors. Still, beyond this, many of the Greek gods are described as sexually promiscuous. No emphasis seems to be placed in any writings on the absence of sexuality in the Greek gods.
Here, I mean asexuality to be the total absence of sexual attraction, with anyone. This is a concept distinct from both celibacy (not having sex for a particular reason) and abstinence (not having sex by choice). For example:
Dionysius is, based on what I've read, abstinent due to indifference to sexuality. There doesn't seem to be anything to suggest that Dionysius doesn't experience sexual attraction, irrespective of whether he partakes in it.
Artemis would count as an example of celibacy, because she's a sworn virgin. (Note: "virgin" means "no sexual relations with men" in ancient Greek works. There's some discussion about whether Artemis was lesbian, but either way, not asexual.)
While there isn't a whole lot of evidence either way, the speculation I've read about whether Athena had sex with anyone seems to have trouble differentiating between Athena as an asexual figure or an abstinent one. (This might make it hard to demonstrate asexuality through the absence of sexual writings.)
The quintessential example, the way "asexuality" is used nowadays, would be if someone in some situation were to turn down a sexual situation - not because they didn't want to have sex with them, but rather because they just didn't feel like having sex, as a whole, with anyone.
Did asexuality as a concept ever appear in Greek writings? If so, is there both asexuality in the Pantheon and asexuality outside of it, or is it just one of the two? I don't expect that the ancient Greeks shared our modern conception of asexuality to a T; however, if it's possible to identify that ancient Greek writings reflect an idea of asexuality comparable to our modern one, that would probably count as an example.