No no no!
The correct expression is I couldn't care less.
The idea is that you are trying to inpart total disinterest in what your opponent is trying to say. So, you are so disinterested that you say I couldn't care less! It's impossible for me to care any less because I'm already at maximum non caring. In other words, nothing you can say will make one iota of difference.
If you say that you could care less, you've admitted to your opponent that they have the power to still affect you. You can still be manouvered into caring less than you do now.
Englishman, on one.