Abdullah Matrood MP3 Quran Off is the best application to listen to the Holy Quran without the need for an internet connection. The audio files can be downloaded and listened offline. This app does not require internet and works perfectly even on weak mobile connections.

It has the ability to play the mp3 files in the background so you don't need to keep the phone screen on. You can also use the volume keys to control the audio.

The audio files are compatible with most mp3 players and can be downloaded directly from the app. You can use this app as a shortcut to listen to the files in the app directly from the notification bar.