The correct phrase is "couldn't care less," but dictionaries and language experts say the Americanism "could care less" is gaining ground and even acceptable in some situations.
Many phrasal verbs can become nouns. For example, you can “start up” a company (phrasal verb) or work in a “start-up” (phrasal noun) – a small company. When a phrasal verb becomes a phrasal noun, sometimes the verb comes first, like “start-up”; and sometimes the preposition comes first, such as “outbreak”.