In Greek mythology, Mneme (pronounced /ˈniːmi/ NEE-mee, or as in Greek Μνήμη), was one of the three original Boeotian muses, though there were later nine. Her sisters were Aoide and Melete. She was the muse of memory.

mneme (n.) mne·me
1. Psychology the retentive basis or basic principle in a mind or organism accounting for memory, persisting effect of memory of past events.
A unit of memory and taken from the Greek mimneskesthai, to remember (and ultimately from Mnemosyne, the Greek goddess of memory.)
2. (capitolized) Class. Myth. the Muse of memory, one of the original three Muses. Cf."Aoede, Melete."

mnemic, a. mnemist

John Laurent in The Journal of Mimetics even suggested that the term meme itself may have come from the work of a little-known German biologist named Richard Semon. In 1904 Semon published Die Mneme (published in English as The Mneme in 1924). His book discussed the cultural transmission of experiences with insights parallel to those of Dawkins. Laurent found the use of the term mneme in The Soul of the White Ant (1927) by Maurice Maeterlinck and highlights its parallels to Dawkin's concept:

Now, the actual phrase that Maeterlinck uses—where he is discussing various theories which attempt to explain 'memory' in termites as well as the other 'social' insects (ants, bees etc.)—is "engrammata upon the individual mneme" (Maeterlinck, 1927, p.198), and according to my dictionary (Webster's Collegiate), an engram is "a memory trace; specif.: a protoplasmic change in neural tissue hypothesized to account for persistence of memory." For what it is worth, Maeterlinck explains that he obtained his phrase from the "German philosopher" Richard Semon.[1] ( [link to jom-emit.cfpm.org]

Laurent suggests that the etymological roots of the term meme may come from mimneskesthai, the Greek term for memory rather than the more commonly accepted root of mimeisthai, or to imitate.