According to Hamel, the Biblical authors were attempting to react to the widespread artistic tradition (unrecorded in literature) that Jason had descended into the belly of a great serpent and through the intervention of the goddess Athena emerged alive from the monster to claim the Golden Fleece. This variant of the myth is recorded in the Douris cup, which I have used as the logo for my website.
Thus, while Jason was a hero for the Greeks, accomplishing feats of greatness through his courage, the Jonah story reinforces the importance of Yahweh above his relatively humble and meek human prophets.
While not all of Hamel’s argument is air-tight (both stories could, for example, descend from older Near Eastern antecedents), it is an interesting way of thinking about the interplay of Greek mythology and Biblical stories.
Bonus parallel: The Jonah story takes place at Joppa (now Joffa), the same place where late versions of the Perseus myth localized his battle with the giant sea monster threatening Andromeda. The bones of the monster (probably a fossilized whale) were available for inspection in Pliny's day according to his Natural History 9.4 (having been shipped to Rome in 58 BCE), and Lycophron (Alexandra 834-42) recorded that Perseus was swallowed by the dragon and killed it from within.
Reference: Gildas Hamel, “Taking the Argo to Nineveh: Jonah and Jason in a Mediterranean Context,” Judaism 44, no. 3 (1995): 341-359.