"nibble" vs. "nibble on"
There’s little difference, as these two citations from the OED, both from the 1980s, show:
She and Roy would nibble on each other.
Encircling her slim waist with a fond arm, the husband of a fortnight nibbles her throat.
Neither describes an act of cannibalism.
Without the preposition is more common, but with the preposition is gaining in popularity.