We have previously stated on this site that it is not permissible for the one who is junub to read Qur’aan or touch the Mushaf, as in the answers to questions no. 10672 and 10984.
Secondly:
Janaabah does not prevent a person from listening to recitation of the Qur’aan, because there is no report of any prohibition on listening. Shaykh Ibn Baaz (may Allah have mercy on him) was asked: Can one who is junub recite the Book of Allah from memory? And if that is not permissible, can he listen to it?
He replied:
It is not permissible for one who is junub to read Qur’aan from the Mushaf or recite it from memory until he does ghusl, because it is proven from the Prophet (blessings and peace of Allah be upon him) that nothing kept him from the Qur’aan except janaabah.
With regard to listening to the recitation of the Qur’aan, there is nothing wrong with that because of the great benefits involved, without touching the Mushaf or reading the Qur’aan from it.
End quote from Majmoo‘ Fataawa Ibn Baaz, 10/152
But in order for it to be permissible to listen to it, it is stipulated that one should not move the lips or tongue in reciting it, because moving the lips or tongue in pronouncing the letters is regarded as recitation, and the one who is junub is not allowed to recite Qur’aan, as stated above.
Ibn Rushd narrated from Imam Maalik (may Allah have mercy on him) that he said: Recitation is that in which one moves the tongue.
See: al-Bayaan wa’l-Tahseel, 1/490
Conclusion:
It is permissible for one who is junub to listen to the Qur’aan so long as he does not move his tongue in recitation.
And Allah knows best.