The Quran was written about 600–700 years after the Bible’s Old Testament and roughly 600 years after the New Testament. It was revealed to Prophet Muhammad in the 7th century CE.
I’d say roughly 500–600 years after the New Testament since the Quran was revealed in the 7th century CE, while most of the New Testament was written in the 1st century. It’s interesting to see how these texts are connected across such a long stretch of history.