Is it possible that the Quran and the Bible were once the same or part of the same book?
History says no to this possibility. For one, the dates of the compositions of both of these books are way different. The Bible was finished in 95/96 AD while the Quran was completed from 610 to 632 AD.
If anything, the Quran borrows from the Bible. When Mohammed was receiving his revelation and writing the Quran he was in conversation with Christians and Jews. He was interested in their religions and how they shared the same holy book.
The Quran contains some of the same historical counts as the Bible, especially in the Old Testament or Hebrew Scriptures that modifies the text according to its own beliefs. I know that the Quran does not deny that Jesus Christ was a prophet.
But he was not the greatest prophet. It floats the idea that Jesus did not actually die on the cross. But this is a historical fact verified and more documents than the New Testament. This is just one example of how the Quran may take the texts of the Bible but change them to suit Islamic belief.
As I mentioned above the shared difference in the dates of the writing and completion of each of these sacred texts shows that they could not have been written at the same time or have been part of the same book.
As with any literature, a text written later can reference and include passages from earlier writings but it cannot contend that it is written at the same time. The older book, the Bible in both the New Testament and Old Testament, would be the one quoted from or referenced by the newer work, the Quran.