Attestation
Median is only attested by numerous loanwords in Old Persian. Nothing is known of its grammar, "but it shares important phonological isoglosses with Avestan, rather than Old Persian." "Under the Median rule Median must to some extent have been the official Iranian language in western Iran.
No documents dating to Median times have been preserved, and it is not known what script these texts might have been in. "So far only one inscription of pre-Achaemenid times (a bronze plaque) has been found on the territory of Media. This is a cuneiform inscription composed in Akkadian, perhaps in the 8th century BCE, but no Median names are mentioned in it.
Some modern research suggest that the so-called Linear Elamite—which still has not been deciphered—may have been written in the language of Medes, assuming Kutik-Inshushinak being original Iranian name of Cyaxares the Great, not a much earlier Elamite king.
Read more about this topic: Median Language