Question:
Is fresh-water eel kosher? I know that the eel is really a fish, with very small scales and elongated fins, so shouldn't this popular sushi fish be kosher?
Answer:
Eel are not kosher, though they seemingly have both signs that demarcate kosher fish: fins and scales.
This is because the definition of fins and scales – as they regard to kosher – are clearly designated by Jewish law. Not every "scale" meets this limited definition. According to Torah law, in order to be considered a "kosher sign," a scale must be easily removable without tearing the fish's skin.
Eel's scales are part of their skin and cannot be removed without tearing the skin.
Best wishes,
Rabbi Baruch S. Davidson

As technologies, skills, and techniques improve Eel scales will become easy to remove without tearing the skin maybe even relatively easier than some kosher fish. May eels become kosher then?
Generally speaking, it would need to be able to be easily removed by hand in order to be considered scales for kosher purposes.
Are eels bottom feeders?