Is it permissible to touch the Mus-haf in order to place it in a clean place if it is found in an unclean place, knowing that I am not in a state of Wudu?

If the Mushaf (copy of the Qur'an) is in a place of disrespect or there is a fear of it being defiled by impurity, it is obligatory to move it from that place. It is not permissible to leave it in such a state. When moving it without Wudu' (ablution), it must be held with a barrier.