Depends on which way you want to say it. I forgot the term describing phrases like that, but I believe the intention behind the phrase is to try and say the person doesn't care at all, meaning they could not care less about something.
People who use the shortened form are often convinced they are right because they are being “ironic” and some even claim it’s the original form. But here’s the entry in The American Heritage Dictionary of Idioms:
This expression originated about 1940 in Britain and for a time invariably used couldn’t. About 1960 could was occasionally substituted, and today both versions are used with approximately equal frequency, despite their being antonyms.
“I could care less” just isn’t logically ironic. The people speaking feel irony, but their words don’t convey it. “I’d buy those jeans” could be ironic if you really meant the opposite: you wouldn’t buy those jeans if they were the last pair in the world. But “I could care less” isn’t used to imply its opposite: that you care more. Thus it is not ironic.
“Couldn’t care less” is a strong statement because it says you don’t care at all, zero!
“Could care less,” whatever meaning you take it to have, does not have that crucial message of zero interest which gives the original saying its sting.
The use of 'could care less' is a widespread phenomenon, primarily in the USA. It seems to stem from people repeating what they think they hear, without thinking about what they are actually saying.
The original expression is couldn't care less, meaning that it would be impossible to be less concerned about the matter, whereas the incorrect use of could care less implies the opposite, namely that the person in question could indeed care less about the matter, so they by definition have some degree of care - almost certainly not what the speaker intended to say.
Language isn't mathematics. Sometimes it evolves like an art form, for instance if something sound a bit snappier, it may get accepted as an idiom. Idioms can be a problematic aspect in language indeed, but there are no laws in any language stating that they are 'wrong'.
An idiom can sound good in its whole, but make no sense once you start to disect it. Now I completely understand your point, but to be honest, I think it's completely irrelevant.
I've gotten to the point that I just do not care anymore. It's become abundantly apparent that the the language will be adapted to the general masses, rather then retaining the original language structure.
I mean, honestly, once you start including omg and lol as words in the dictionary, as well as including words that started off as slang for searching for something online, you should realize the language has already been shot to hell.