Praise be to Allah.
The Glorious Quran should not be touched by anyone except those who are purified . Allah says (interpretation of the meaning):
“Verily, the Mushrikun (polytheists, pagans, idolaters, disbelievers in the Oneness of Allah, and in the Message of Muhammad) are impure.” [Al-Tawbah 9:28]
On this basis, the non-Muslim should not be permitted to touch the Quran, whether he is a Christian , a Jew, a Buddhist, a Hindu or anything else. But it is permissible for him to listen to the Quran on radio or TV, or from tapes, and it is permissible for him to read the translations of the meanings of the Quran which are available in different languages.
And Allah knows best.