Allah has referred to the Quran as a Book, which by definition is something written, in many Quranic passages. One example would be (what means): ( By the Mountain, and by a written Book (the Quran), written in pages of a book spread out ) [52:1-3]
The Prophet (may Allah raise his rank and grant him peace) said, what means, (( Do not travel with the Quran, since I can not guarantee that the enemies would not get a hold of it. )) [Muslim]
Quite obviously, the Messenger of Allah (may Allah raise his rank and grant him peace) was not referring to the Quran memorized in their hearts or the Quran in al-Lowh al-Mahfooth (the Preserved Tablet)! He was referring to the mus-haf, the written Quran, and he explicitly called it “the Quran”.
‘Umar ibn al-Khattaab, the second Caliph of the Muslims (may Allah be pleased with him), had no problem with this expression either, as it is narrated that he wrote to the governors in the various lands under his rule, following the best example, saying: “Do not travel with the Quran to enemy lands, since I fear that one of them might get a hold of it.”
Aboo Bakr As-Siddeeq, the first Caliph, placed Zayd ibn Thaabit (may Allah be pleased with them both) in charge of compiling the scattered writings of the Quran into one mus-haf, as the era of Divine Revelation had just ended, and the Quran could not have been compiled into one book while it was still coming down.
Zayd said about the gravity of this task:“I swear by Allah, had they placed me in charge of moving a mountain, it would not have been more heavy than the task he ordered me with of compiling the Quran (into one mus-haf)!”
During that time and ever since, this event is referred to by the Muslim scholars as Jam’ al-Quran, or the compilation of the Quran (into one mus-haf).
‘Uthmaan ibn ‘Affaan, the third Caliph (may Allah be pleased with him), said, “I do not like that a day and night pass except that I look at the Speech of Allah, the Mighty and Majestic.” (meaning: reading the mus-haf)
‘Alee ibn Abee Taalib, the fourth Caliph (may Allah be pleased with him), said, “May Allah have Mercy on Aboo Bakr, for he was the first one to gather the Quran between two book covers (i.e. in one mus-haf).”
‘Abdullaah ibn Mas’ood (may Allah be pleased with him), was reported to have said, “Verily, this Quran in front of you is about to be snatched away from you!”
His student asked, “How could it be snatched away from us while Allah has made it firm in our hearts and we have recorded it precisely in our mus-hafs?!
He replied, "It (the Quran) shall be taken up in one night, and everything in the hearts shall be snatched away, and everything in the mus-hafs shall go, and the people shall become needy from it (the event). Then he recited, what means: ( And if We wanted we could take away that which We revealed to you ).”
‘Ikrimah ibn Abee Jahl, one of the Companions (may Allah be pleased with him), used to hold the mus-haf to his face, saying, “The Book of My Lord, the Mighty and Majestic, the Speech of My Lord, the Mighty and Majestic!”
Yusuf Estes And the Quran 