I don't/couldn't give a monkey's

not give a monkey's

To be disinterested or indifferent. This version is truncated to avoid the expletives that often follow "monkey's." If you think I care what he says, you're wrong—I don't give a monkey's! I know you couldn't give a monkey's about your room being clean, but can you at least pick the clothes up off the floor once in a while?
See also: give, not
Farlex Dictionary of Idioms.

I don’t/couldn’t give a ˈmonkey’s

(British English, slang) used to say, in a way that is not very polite, that you do not care about something, or are not at all interested in it: To be honest, I couldn’t give a monkey’s whether you go or not.
See also: give
Farlex Partner Idioms Dictionary
See also:
  • not give a monkey's
  • not give a continental
  • continental
  • freeze
  • give (one) the freeze
  • fingers crossed
  • you('ve) lost me
  • you've lost me
  • follow (one) to the ends of the earth