Background: "Eyes of a hawk" is a far more common phrase. Google ngrams has 0 results for "ears of a hawk" and there are half as many results for it on Google and Bing.
- "Ears of a Hawk"
- "Eyes of a Hawk"
Therefore, if you said "Ears of a hawk" with a comedic intent, this could be an anti-proverb ("eyes of the hawk" is admittedly not a direct proverb, but it would be fair to describe said hawk as "proverbial" - see definition #5). It isn't really a malapropism as you aren't mistakenly substituting ears for eyes. The closest terms to exactly describe this figure of speech would be a Goldwynism or Yogiism, which seems to just mean "something funny these famous people might have said."
My point is that if you were to describe someone as "She has the ears of a hawk!", you would probably be perfectly well understood by most English speakers as meaning "She has superior hearing."
If you want to strive for correctness over comedy or colloquialism, there are many animals with exceptional hearing to choose from. But that can also be made humorous; deriving humor from exacting explanations is apparently called 'reframing.' As the other answers here have proved, there is not a single most accepted animal for hearing comparison, so you really can pick your favorite.
One other side note, you could make a pun on a poor fellow with very hairy ears by saying "He has the ears of an arachnid!" or "He has ears like Trichobothria!" The joke is that spiders don't have hearing organs like mammals, but detect vibrations with nerves connected protruding hairs called trichobothria. As you can clearly see from this youtube video of a spider dancing to a saxophone, arachnids can hear just fine with these organs.