"could care less" is a shortening of "could not care less", and the latter phrase is correct. the words themselves don't mean anything any more, it's a stock phrase.
i think the sentiment is, "I care so little that I don't even want to use all the words needed to say how little I care".
i think the sentiment is, "I care so little that I don't even want to use all the words needed to say how little I care".