There is a long tradition of songs from the movies becoming jazz standards. This is probably because once the songs become familiar to the public, jazz artists find the public more receptive to hearing those songs with a jazz treatment.
There is similar phenomenon where children's songs have become standards. For example, "A Tisket, A Tasket", and "It's Not Easy Being Green". In the present case, we have a song from a children's movie, "An American Tail". "Somewhere Out There" has been performed by artists from Mickey Dolenz of "The Monkees" to Linda Ronstadt, Kenny Loggins, numerous jazz big bands and many small combos.
Here is an arrangement with a smooth jazz feel. The song is AABA form with few complications. Near the end of the B section, you find a single 2/4 measure. Other than that, it is a rather normal flow with a small extension on the last A section.
In this arrangement, after the choruses, we have includes a little 4-bar vamp for some extra fun.