Aah, the memories, Fifa 64 was my very first request on here, it was the reason I joined hcs64 originally. If I recall correctly, I was told it was unknown how to rip the music files, because the way they were encoded was not standard, if it was known how to do it we'd have gotten the rip back then. Since it was bugging me that I couldn't listen to the songs unless I fired up the game, I made a FLAC gamerip that can be downloaded from khinsider (or as mp3), and at least you can listen to the songs at my musycaramel channel on youtube. I do love those songs.
UPDATE: On July 27th 2025, 6 days after my last post, someone uploaded a rip of all audio files from the game! Unfortunately it's a bunch of unplayable files and a mysterious midi bank file, so nothing gained, but this is as close as we've gotten to fulfilling my December 26, 2009 request (which I did as Vytron) of this!