Convert MP4 to APK

Since you cannot directly convert images or videos to APK format, it is, per se, not possible to convert MPEG-4 Videos to Android Package Files (.mp4 to .apk conversion). 

You could, however, use specialized apps, such as the Live Wallpaper Creator, which allow users to generate rich/animated wallpapers for Android devices from images and/or videos. Such wallpapers are typically created as APK files, i.e. programs, which can be installed and run on an Android device replacing your current wallpaper.