u/Arm_Enkidu

The Alexander Romances are said to have been influenced by the Gilgamesh stories. [1]

The Quran recounts the story of Dhul Qarnayn, "Possessor of the Two Horns" [2]

In the Epic, Gilgamesh cuts off the horns of the Bull of Heaven and takes possession of them. Gilgamesh also travels the world like Dhul Qarnayn. [3]

We see some vital pieces of information preserved in the Islamic corpus:

Al-Azraqi and others mentioned that Dhul-Qarnain embraced Islam at the hands of Ibrahim (Abraham) (Peace be upon him) and that he circumambulated around the Ka bah with him and his son, Ismail (Peace be upon them). Also, it was narrated after Ubaid Ibn Umair and his son, Abdullah and others: that Dhul-Qarnain set out on foot to perform Pilgrimage. Upon hearing this, Ibrahim (Peace be upon him) welcomed him and invoked Allah for his sake and gave him advice as well. In addition, Allah the Almighty subjugated for Dhul-Qarnain the clouds to carry him wherever he wished. Allah knows best!
[4]

The 8th century Syriac Christian theologian Theodore bar Konai mentioned "Gmigmos/Gligmos" as a king who was Abraham's contemporary. [5]

Abraham came from the Sumerian city of "Ur" that is a focal point of the Epic of Gilgamesh. By Biblical geneological dating, Abraham's birthdate lines up quite closely with the best guess of the Mythological Gilgamesh's lifetime.

A report attributed to 'Ali states that Dhul Qarnayn was selected by Allah after the flood of Noah:

"Dhu’l-Qarnayn was an exalted servant of Allah. His name was Ayaash. The Almighty selected him after the Flood of Noah and gave him suzerainty over the surrounding areas of Northwest Africa in the two centuries. The people hit him on the right and he was martyred by it. Then after a hundred years the Almighty raised him to life in the areas of East. This time the people hit him on the left side of his head and he was martyred. The Almighty raised him again after a hundred years and the lieu of the strokes he had suffered granted him a pair of outgrowths with a space between them. And gave him Kingship, Prophethood and miracle." [6]

In the Epic, Gilgamesh meets Utnapishtim, the man who survived the great flood by building a boat.

In an account attributed to Umar bin Khattab, Dhu al-Qarnayn is said to be an angel or part angel. [7]

Gilgamesh is described as two thirds divine and one third human.

The early Muslims possibly got this information from speaking with People of the Book about Dhul Qarnayn. In my opinion, this implies that there were probably oral stories where the King "Gligmos", a contemporary of Abraham is the one to go through the journeys that Alexander does in the Syriac Alexander Romance. This is because Muslims possibly asked the People of the Book about the story of Dhul Qarnayn, and they told them "This sounds like the story of that King that met Abraham", which is why these reports from the Salaf show up in the Islamic corpus.

So, the quotes below are quite relevant:

Marianna Klar writes:

"In order to prove a direct derivative relationship between the two traditions, both van Bladel and Tesei emphasize the similarities and gloss over the disparities between the Qur'an and its supposed contextual foil. The Qur'anic exemplum is highly allusive, and makes no reference to vast tracts of the narrative line attested in the Neshana. Where the two sources would appear to utilize the same motif, there are substantial differences to the way these motifs are framed. These differences are sometimes so significant as to suggest that the motifs might not, in fact, be comparable at all."

She further states:

"It seems more likely, therefore, that it is the Neshana that is the anomalous source here, and the Qur'an simply does not depart from an already established theme. The cumulative instances of mismatch between the Qur'anic exemplum and the Neshana cast doubt on the accuracy of Tesei's conclusion that 'the Syriac text is the direct source of the Qur'anic pericope', and a directly derivative relationship between the two traditions has been assumed rather than established."

— Marianna Klar, Qur'anic Exempla and Late Antique Narratives

Travis Zadeh similarly notes:

"At a linguistic level the significant instances of divergence between the Quranic text and the Neshana put into serious question the exact relationship between the two accounts. There is much to suggest that eschatological discourses on the life of Alexander and Gog and Magog were widely diffused throughout the seventh century both orally and textually. It is thus tenuous to attempt to historicize the Quranic account using material that may not have been a direct intertext of the Quran."

— Travis Zadeh, Quranic Studies and the Literary Turn

Likewise, Stephen Gero writes:

"The apocalyptic element is very pronounced in this work. Alexander is depicted as a pious, proto-Christian instrument of God, endowed with the gift of prophetic utterance. Several features of the text also occur in the Koranic narrative (...). But, although this has been proposed by Nöldeke and often repeated since, the work also does not qualify as a direct source for the 'two-horned' Alexander of the Koran, at least not in its present form."

— Stephen Gero, The Legend of Alexander the Great in the Christian Orient

Wheeler here addresses the methodological approach itself not just the corpora:

It is tempting, given the perplexing character of Q 18:60-82, to make connections between the Qur'an and other stories circulating in roughly the same period. Q 18:60-82 is rich in symbolism and possible allusions to other late antique motifs. The explanation given to these verses by Wensinck, and followed by the bulk of subsequent scholarship, is mistaken, however, in its lack of adequate attention to the dates and provenance of the so-called sources for Q 18:60-82. Wensinck's explanation is self-serving in that it supports the assumption that the Qur'an is comprised of Jewish and Christian materials both garbled in transmission and confused by Muhammad. By demonstrating that the admixture contained in the Qur'an can be understood only with knowledge of the original versions of the stories upon which it is dependent, scholars such as Wensinck were able to put themselves in a privileged position vis-à-vis other interpretations of the Qur'an. This approach to Q 18:60-82 results in an erudite-sounding explanation but misses a number of crucial points.

Further, he adds:

It is important to recognize the Qur'an sharing in larger culture of late antiquity, but it is unfortunate to ignore the pivotal role played by the early commentators in identifying and appropriating certain late antique motifs to the understanding of the Qur'an. Q 18:60-82 is not necessarily derived from the Alexander stories. On the contrary, a more discerning examination of the different texts show that the later recensions of the Alexander stories are dependent upon the Qur'an as understood through the medium of early Muslim commentators.

[1] Tesei, Tommaso (2010). "Survival and Christianization of the Gilgamesh Quest for Immortality in the Tale of Alexander and the Fountain of Life"

[2] Surah Al Kahf

[3] The Epic of Gilgamesh

[4] Stories of the Quran, Ibn Kathir

[5] Jeffrey H. Tigay, The Evolution of the Gilgamesh Epic, 2002

[6] Tafsir Mohammad ibn Masoud Ayyashi

[7] The Report on Humans, Al Maqrizi

And check out u/Aromatic-Army-7755 's great post:

https://www.reddit.com/r/MuslimAcademics/comments/1u3kict/important_clarifications_on_the_dhul/