andy, you cannot store "audio" in ram nor (ep)rom ... whatever connection you use (spi, i2c, parallel..) ... you can only store bit's, nibble's or byte's
in order to do so, you first need to perform AD conversion so you "digitize" the sound and then you store the array of values in the ram/(ep)rom...
lot of micro controllers have AD conversion unit embedded but most of those are not "fast" enough to sample sound (you need to have 44100 samples per second to get CD quality, around 4-8000 samples per second to get "usable" sound) so you might have to get either "high end" uC or some specialised AD chip.
in order to reproduce sound, again, you have to perform DA conversion which is bit easier to do (you can build simple resistor ladder DA converter quite easy or use specialised chip).
one thing to consider is bandwidth. in order to sample and store sound you need to be able to store it quickly enough or your buffer will overrun .. to explain, if you have 8000 samples per second, this means that you will have 8Kb of data to store every second. Some i2c eprom's cannot store data that fast (64KBps is lot of bandwidth) so you might have to go with some SPI or parallel storage device. You will fetch this data into uC and then store hence uC can use available ram to buffer the data before it is written to external storage. With slow storage, length of the sound sampled will be limited to the available ram on the uC (so with 8Kb available on uC with 8000 samples per sec, you will be able to store only 1sec of sound data)
note that there are specialised chips that do this for you (sample, store, retrieve, reproduce sound) and they are not expensive... IIRC the mp3 encoder/decoder chip with MMC card used for storage with SPI connection to uC was ~20$ (kit board with mp3 chip, mmc slot, sound out/in port, few elcos ...) maybe that would be better solution ?
example
**broken link removed** schematic:
https://www.electro-tech-online.com/custompdfs/2008/09/easymp3_schematic_v101.pdf
**broken link removed** schematic:
https://www.electro-tech-online.com/custompdfs/2008/09/smartmp3_schematic_v101.pdf