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 is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
There is no harm, Allaah willing, for a person in a state of major impurity to listen to the Quran, because being in a state of major impurity is not an obstacle which prevents from listening to the Quran. There is a difference (for a person who is in a state of major impurity,) between reciting the Quran and listening to it, and there is no need to inform your friend that you are in a state of major impurity.
It should be noted that a Muslim should take the initiative to perform Ghusl. The Prophet said: "The angels do not approach three kinds of people: the corpse of a non-Muslim, a person who applied Khalooq, and a person who requires Ghusl (a ritual bath) because of sexual defilement until he performs ablution." [Abu Daawood] [Khalooq is a kind of perfume produced of saffron and other ingredients]. Ablution reduces the state of major impurity but does not remove it.
Allaah Knows best.