Could Care Less Attitude?

If you say that you couldn't care less about someone or something, you are emphasizing that you are not interested in them or worried about them.

Is I could care less correct?

"Couldn't care less" and "could care less" are both used to mean someone doesn't care at all, but English teachers and grammarians will say that only "couldn't care less" is correct, so that is what you should use in formal or academic writing.

What do you call someone who could care less?

apathetic. couldn't care less. neutral. not give a tinker's damn. unconcerned.