So there's some stories of Jesus in the Muslim holy book, big deal.
And they believe he is the Messiah, born of a Virgin, and that he will come again at the end of the world, and he is referred to as a great prophet....
That is true, however their interpretation of messiah is not the same. Coming back to the OP, the Quran instructs Muslims to ask the 'people of the book' if they do not know.
"And We sent not before you, [O Muhammad], except men to whom We revealed [the message], so ask the people of the message if you do not know. "Surat 21 Ayat 7
What answer would they receive from the people of the book except Isaiah 7:14 "Therefore the Lord himself will give you a sign: The virgin will conceive and give birth to a son, and will call him Immanuel." Immanuel = God with us
I wonder if Muslims realise the implications of Surat 19:20?