We can identify with reasonable certainty where Alhazret derived his description of kthulu (خذولُ) as: being far older than the human species, coming to the Earth ages ago from "out of the sky" (amongst the stars), being of gigantic size, with scaly skin, leathery wings, and prodigious claws on its fore and hind limbs. Most disturbingly, having a mass of writhing serpentine appendages where one would expect to find a head or face.
Alhazret's parents, being typical Sana'a natives in the 7th century, only converted to Islam as adults. So, Alhazret almost certainly would have been familiar with this image as an older representation of ash-shaytan (الشيطان). Being fluent in Greek, it is likely that Alhazret also read descriptions of this figure in such ancient texts as _Ἀποκάλυψις Ἰωάννου_ where we find Σατανᾶς described as a “δράκων μέγας” and as “ἔχων κεφαλὰς ἑπτὰ”.
We also can conclude that Alhazret derived the name “kthulu” from what was already an extremely familiar designation of ash-shaytan (cf: “لقد اضلني عن الذكر بعد اذ جاءني وكان الشيطان للانسان خذولا”).
Of course this begs the question of why he chose that particular designation and that specific representation out of all the many which existed in his day. Alhazret himself seems to indicate that he learned that these were the “true name” and the “true form” of this ancient god in a series of bizarre dreams. He also claimed that the (non-human?) leaders of the cult dedicated to this god in Iram dhat al-'imad (إرَم ذات العماد) confirmed this information. This last claim is of course fantastic and either an example of Alhazret’s tendency to spin fanciful yarns or perhaps evidence of mental disorder.
In any event, Alhazret seems to have seen himself as preserving the lore of an ancient cult from the darkest and most remote of the “Days of Ignorance” (Jahiliyyah جاهلية).