They are listed in the MM as Mind Flayer Medium aberration , lawful evil and Intellect Devourer Tiny aberration , lawful evil and there enough lore to make me believe that they are could be from the Far Realm so I have no trouble believing they could be related to a Great Old One.

Chulthu as the god of the Mind Flayer

Were Illithids inspired by Cthulhu?

Mind Flayer Origin