In conversation if someone pitches something to you but you're not entirely convinced, can you ask for more details by saying "intrigue me"?
Grammatically speaking, there's nothing at all wrong with imperative "Intrigue me", but it seems likely OP has misunderstood what the verb to intrigue actually means. From OED...
(transitive) To excite the curiosity or interest of; to interest so as to puzzle or fascinate.
The meaning OP wants to convey is normally expressed by "Convince me". But here's an example where it really does mean "Do something to excite my interest"...
(New York Magazine "Lonely Hearts" column, 1985)
Passionate, Brilliant, Bizarre — Woman, 29.
I am quite wicked, beautiful and successful. I dare you to intrigue me.
No. You are intrigued. The other person does not intrigue you.
You could rephrase it as:
I am intrigued. Please tell me more.
But that wouldn't necessarily have anything to do with being convinced, more to do with your curiosity being aroused.
To correctly rephrase your sentence I would go with:
I don't think talking about being "intrigue[d]" sufficiently indicates to the other person in the conversation that you're not convinced.
It is perfectly acceptable, and rather common, to simply state that you're not convinced.
If you did insist on using the word "intrigue" then you definitely wouldn't say "intrigue me"; it could confuse the other person as it's an unusual construction. Instead you would probably say "I'm intrigued", which, to be honest, is a closer approximation to "I am interested", and errs closer to suggesting that, actually, you are rather convinced.
I guess you could be more explicit with "make me intrigued", but after all it's a conversation, so "intrigue me" should be enough to convey your meaning.