Question: It is permitted to place the Mus-haf upon the ground or upon the carpet in a Masjid?
Answer: That which is obligatory is to raise the Mus-haf and to show it respect, except in a case of necessity [when one is compelled]. And Allaah is the Granter of success.
See Fat-h ar-Rabb il-Wadoodi Fil-Fataawaa war-Rasaa’il war-Rudood, vol. 1 p. 140, of Allaamah Ahmad b. Yahyaa an-Najmee (rahimahullaah).