"Let's talk about ... "? Do you mean "I would like to speak to you about something."? As far as I know it's not implemented yet, unless it's used in multiplayer (which I haven't tried).
There's no way yet to ask the AI to destroy their starbase. It's been asked for, but if it ever happens it'll be later than next Thursday. All you can do in the meantime is try to buy it or declare war and destroy it.
