I would actually speculate that apart from the above iconoclastic view of Jesus from the orthodox belief, perhaps Judaism had a greater influence on Islam, and Islam's general view on the non-godliness of man. Islam and Judaism share almost similar prayer times, similar prayer styles, extremely parallel belief systems, etc due to the proximity of Jews in Arabia (Medina [Yathrib]
was a largely Jewish city pre-Islam). But while Judaism chose to reject Jesus as even a prophet outright, Islam sought to reconcile the view by keeping him a prophet, perhaps because the Roman Empire under Heraclius was still very dominant.
It is important to note that Islam was created as a very administrative religion rather than a philosophical one, partly because Muhammad wanted to see it being adopted in 3 key regions. He sent emissaries to Heraclius the Elder (at Constantinople), who briefly considered the proposal, to the Patriarch of the Copts (at Alexandria), who amicably received it, preserved it (till today) and sent back his own friendly missive of rejection [1], and to Khusrau of the Sassanid Empire, who tore up the letter. So I doubt that Muhammad actually gave much effort to philosophical aspects such as Jesus or Ahura Mazda, and simply chose to borrow the history from nearby religions while reconciling them with the core that is Islamic monotheism. In fact, Muslims actually have four books they consider holy - the Torah, the Zabur (Psalms), the Injeel (Gospel of Christ) and the Quran (Revelations to Muhammad).
[1] https://en.m.wikipedia.org/wiki/Al-Muqawqis