No - fish dont simply have the brainpower. A fish's mind is VERY simple and VERY small compaired to the human mind. Dreams require imagination
. Our minds subconsciously create an environment (places, cities, etc) and objects so complex and thorough that we actually believe they are real when we are in our dream. I dont think a fish's mind is capable of that. Perhaps other mammalian animals can dream (primates for example), but not fish.
(Scroll down to "Central nervous system
PS: I just realized I sound like one of the guys from Inception