I'd like a word with you
I'd like to talk to you, perhaps to issue a warning or reprimand. A: "Aunt Karen let me have ice cream for dinner!" B: "Is that so? Karen, I'd like a word with you."
I'd like (to have) a word with you. and Could I have a word with you?
I need to speak to you briefly in private. (The alternate entry is also used with can or may in place of could.) Bob: Can I have a word with you? Sally: Sure. I'll be with you in a minute. Sally: Tom? Tom: Yes. Sally: I'd like to have a word with you. Tom: Okay. What's it about?