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?
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