All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is permissible to recite from the Mus-haf while praying, according to the preponderant opinion of scholars. If one recites from a Mus-haf in prayer, let him, during Rukoo‘ and Sujood, place it on a shelf or a rack or so to be near the praying person, in order to give the Mus-haf its due honor and exaltation. An-Nawawi said, "There is consensus among the Ummah about the obligation of honoring, exalting and maintaining the Mus-haf absolutely."
So, it is not fitting for the praying person to hold the Mus-haf with his hand and prostrate on it, nor is it allowable for the praying person or anyone else to place the Mus-haf on the ground. It was narrated on the authority of Ibn ‘Umar that he said:
"A group of the Jews came to the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, and called him to (meet them at) Quff (a valley in Al-Madeenah), and he came to them in the house of Midraas (where they used to study the Torah), and they said to him, "O Abu Al-Qaasim! A man from among us had an illegal sexual relation with a woman: so, please, decide their case." They placed a cushion for the Messenger of Allaah, sallallaahu ‘alayhi wa sallam, to sit on. Then, he asked for the Torah and it was brought, thereupon he took the cushion from underneath him, and placed the Torah on it and said, "I have faith in you (as being a Divine Book revealed by Allaah) and in Him (Allaah) Who Revealed you." Then he said, "Bring me the most learned one among you." A young man was brought to him (thought to be ‘Abdullaah ibn Sooriyya)..." [Abu Daawood]
If the Prophet, sallallaahu ‘alayhi wa sallam, placed the Torah on the cushion by way of honoring it, then, what (would you think) about the Mus-haf?
Allaah Knows best.