From the Merriam-Webster site:
Could vs. Couldn't
We define could care less and couldn’t care less on the same page, with the single definition “used to indicate that one is not at all concerned about or interested in something.” We do not put these seemingly disparate idioms on the same page in order to save space, or so that we might cause you pain. We do it because one is simply a variant of the other, and they are used in a synonymous manner.
There is little doubt that couldn’t care less is the older form, although no one is certain where this came from. There has been speculation that it is British in origin, and that American soldiers returning from World War II brought it to these shores. While it may indeed have come from the United Kingdom, there is clear evidence that couldn’t care less was in use prior to the 1940s.