All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
According to the view of most scholars, a person in a state of major impurity (Janaabah) is forbidden from reciting the Quran, whether he is reciting from his memory or by looking at the Mushaf.
An-Nawawi said in al-Majmoo’:
"Our view is that it is forbidden for the person in a state of major impurity or a menstruating woman to recite the Quran, whether it is little or much, even if it is only few verses. This is the view of most scholars." [End of quote]
However, it is permissible for a person in a state of major impurity to look at the Quran and recite it by his heart without touching the Mushaf (the Arabic copy of the Quran) or reciting it by the tongue.
The Fiqh Encyclopedia reads:
"As for a person in a state of major impurity and a menstruating woman, they are forbidden from reciting the Quran, but they are permitted to look at the Mushaf and recite it by the heart only." [End of quote]
Allah knows best.