Although Muslims believe in the immaculate conception of Jesus (`Isa), Muslims do not celebrate Christmas. Besides many Muslims aversion to celebrating birthdays of anyone, there is no historical basis that Jesus was born on December 25th.
It is known, however, that the pagan Romans blended many of their traditions into the religion of Jesus. December 25th during the time of the pagan Romans was the Day of the Unconquered Sun in which the pagan Romans worshipped many gods including forces of nature.
Closer to monotheism, Mithraism, a form of Zoroastrianism, teaches that Mithra, who was believed to be the Son of G’d, was born on December 25th.
Eastern Orthodox Christians currently celebrate Christmas on January 7th.
Either way, it is safe to say that Jesus was not born on December 25th and is a day influenced by polytheism practices that came before Jesus.