Dreaming of eels often associate with slimy and slipperiness. To interpret the dream with any positive meaning, you must be able maintain a grip on the eel in your dream, otherwise your fortunes will be fleeting.
Eel in a dream may also reflect an ongoing commitment that the person does not feel especially connected to and might try to escape. This could be fairly innocuous, such as neglecting their living room, or it could be something significant like unhappiness at work.
Eels were believed to be able to escape from capture by slithering through the smallest of holes, so in dreams they may signify difficulties easily evaded or gotten out of.