The storytelling ape (one word) would be simius fabulator. (You could also do simius fabulans if you want a parallel construction; the former is more “the storyteller ape” and the latter “the ape telling stories”).
Story-loving (hyphen) would be simius amator fabularum or simius amans fabulas You could perhaps make up a word meaning “story-loving”; simius amafabulas or something, but I like that less.
Both of these are the masculine form. Simia is the feminine. Pan is neo-Latin; in Latin, it would be the god Pan, whom you presumably don’t mean.
Some cautions: “simius” is often used as a derogatory term for a human that merely imitates, and “fabulare” also just means to talk, so without context it doesn’t necessarily clearly mean what you want it to mean.