That was the theory of Milman Parry, who made visits to Yugoslavia and other areas of Eastern Europe where oral poetry was still widely practiced, and noted similarities between the form of the existing traditions and that of Homer.

I haven't studied it seriously since college, but among evidence to support this theory is the idea that many of the titles used to describe the heroes may have been formulaic mnemonic aids that the singer/poet could keep in their back pocket and pull out during improvisation to fit the required meter.