Is it permissible to place religious tapes bearing the name of Allah in a closed drawer near the ground, with sofas in the same room such that the level of the feet would be above the tapes when seated on the sofa?

There is no harm in placing the foot on something elevated, such as a step or a box, containing religious tapes or books. If they are placed there with the intention of venerating them, that is even better. It is known that Quranic tapes and CDs do not have the same sanctity as a printed Mushaf, and it is permissible for a menstruating woman or someone in a state of ritual impurity (junub) to touch them.