In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
Answering your question, Sheikh Mustafa Umar, President of California Islamic University, states:
A Muslim should not bring the Quran into the bathroom. This ruling applies to the Quran being written on paper.
As for a digital recording on cell phones, its existence is on a memory chip along with thousands of other programs. This recording is not written in any form like a piece of paper.
Therefore, it is allowed to enter into the bathroom with a computer chip that happens to contain a recording of the Quran, since it is not considered to be a written copy of the Quran at all.
However, you should not listen to it while in the bathroom.
Almighty Allah knows best.