Everything points to the fact that you cannot directly convert gif to mp3, via gif to mp3 conversion. GIFs are images and MP3s are audio files. But you may be looking for a way to get the picture into mp3 that will be shown during playback. You need some mp3 tag editor or music management software like e.g. Helium music manager. With this tools, you can edit information about mp3 song, add pictures and texts or more info into mp3 file and save it.
Open GIF file Open MP3 fileA multifunctional media converter for Windows