I doubt they could fit any storage on airpods, they're already filled for batteries. Apple watch is the companion for working out without your phone and that has onboard storage
I have the Bragi Dash which has 4GB of storage. Because their bluetooth is pretty crummy, they actually work best as an in-ear mp3 player, no phone required. It's pretty nice for running because carrying a giant phone in running clothes is a nuisance.
The Samsung Gear IconX (last year's model) had 4 GB of storage. However it was useless to me as I no longer manage my own MP3 files. I use Pandora/Spotify/Google Music/etc.
If Apple adds storage, they hopefully will do it in a way where it's easy to "cache" playlists or albums easily without having to manage files.