Omar Khayyam is not a sufi. This is my conclusion.
In the “Rubaiyat”, Omar Khayyam compares our life to travels. Sufic poets do it in the same way. Or Omar says, “Enjoy the moment”. The word “moment” —‹hal› in Persian— is also used by sufis. And Jan Rypka, in his famous work “A History of Iranian Literature”, said that Omar followed the same path as Avicenna, which bore a strong resemblance to the Isma'ili doctrine and sufism. These things explain why he had long been regarded as a sufi by many people. Nevertheless, he was not a sufi.
Firstly, we can hardly apply the allegory of the mystical Iyric to the poem of Omar Khayyam. Inhis rubaiyat the word ‹sharab; wine›, for instance, cannot be understood that it means the ecstatic experience due to the revelation of the True Beloved.
Secondly, Omar's ‹nisti› or ‹adam› which mean nothingness do not accord with the concept of so-called ‹fana;› annihilations or ‹Das Nichts› in the West.
Thirdly, his notion of ‹falk; the sky› is closely akin to the one of us Japanese. It differs from ‹xoda; Gods› in Islam.
Lastly, the greatest differrence between the Omar's thought and the sufism is Love for God. A sufi loves God fiercely as if he were a youth who was caught in a net of love. We can't feel such a passion in the rubaiyat of Omar Khayyam.
Thus I think he is not a sufi. However, we can also say that he is not a simple atheist. There is no proof that he completely denied the unique Reality. He merely does not use the word of God like Plotinos.
P. S.; I wrote this monograph using Heron-Allen's “The Ruba'iyat of Omar Khayyam” as a reliable text.