Anyone who thinks about the words in this expression has to agree in the end that only 'I couldn't care less' makes sense. It means that it would be impossible for you to care any less than you already do - you already care NOTHING about whatever it is.
But, as happens sometimes, the phrase has been shortened in colloquial speech by people who didn't listen to, or grasp, the full phrasing, and now the shorter version, though obviously senseless. has, in American English, become the norm.
In British English we still say 'couldn't care less'.