When you say he's "not interested" in finger foods, what do you mean? Will he eat them off your fingers? Does he pick them up at all? It takes some time for babies to get the hang of finger foods, so it's possible that his lack of interest may just be a matter of him getting used to them.
How long has this been going on? What does his daily routine look like? How is his breast/bottle intake? Hopefully with some more information, we might be able to find some answers!