could care less
Clipping of couldn't care less, which is literally accurate (having no ability to care less).
- (idiomatic, US) Lacks interest; has apathy towards.
1967, American Institute of Cooperation, American Cooperation:
- Farmers knew that dead fish made plants go better. They could care less about why that happened. Scientists could not sleep until they found out why.
1995, Orrin Hatch (ed.), Trademark Counterfeiting: Hearing Before the Committee on the Judiciary, U.S. Senate:
- We do work...to develop some strength and testing standards so that the industry can be assured that safe products are being produced. The person who is doing a knockoff could care less about that, and so they will just produce the product with virtually no field or laboratory testing...
- 1999, Christopher Shays, Combating Terrorism: Role of the National Guard Response Teams 
- As someone who lives 30 miles away as the crow flies...from New York City, I could care less that New York City or New York State has a sense of jurisdiction.
2003, Donna Hill, If I Could, page 58:
- Maybe it wasn't only time to move away from a job that was killing her spirit, but from people who could care less about her as a person, who saw her only as the good girl from next door, the one who would never do anything to upset anyone, who totally underestimated her.
- Linguists consider this expression acceptable because it is widespread and because it is an example of similar developments in English and other languages: "In Defense of I Could Care Less"
- Some prescriptivists, including some English professors, consider it a malapropism because the literal meaning of this version is the opposite of the intended meaning: Common Errors in English Usage, (2003, Brians) - Page 49 proscribes this very common cliché as being "careless". The recommended form is "I couldn't care less" or the even less common and more formal form "I could not care less".