the Fatwa Department Research Committee - chaired by Sheikh `Abd al-Wahhâb al-Turayrî
When you are in a state of minor ritual impurity (requiring wudû’ only) you may not touch the written Qur’ân. You may recite it from memory and - Allah willing - you will receive a reward for that.
You may not even recite the Qur’ân when you are in a state of major ritual impurity (janâbah) requiring a full bath.
And Allah knows best.
Source: Islam Today