The answer depends on whom you ask. According to most grammarians, this expression is logical and correct only with couldn’t. If a person says, “I couldn’t care less” about something, it means that the amount of care and concern they have about something could not be any less, any lower. This makes sense. Therefore when someone says I could care less, it should mean the opposite, that they are concerned.

However, if you listen to native speakers, you will hear people saying “I could care less,” and you will know from the context and tone of voice that they mean they are not at all interested or concerned. So while the expression with could may not be as logical, it is used. And if you’re interested in understanding actual usage, like many linguists and learners, you should definitely be aware of both forms.