Unless you use an external EEPROM or you want to store very short audio, I don't think you'll succeed. An ATMega 16 has only 512 bytes EEPROM.
If you want do some experiments, you can follow a quick and dirty path: sample at fixed intervals the audio level at an ADC port and store raw data. You can play them later with an ADC.
Note that, even to attain a poor quality result, you need to sample each 250-300 us. Mega16 ADC is able to do so, but you roughly need 4kbyte for one second of record.
For serious results, I recommend to move to a bigger and more powerful device, such as Atmel UC3 (core AVR32), in this case you can compress the audio with a software vocoder.