I know that some people use this when they want to say that they have no idea about that particular thing. But the thing is that, in my case none of them are native English speakers. So I thought it's worth to ask if natives use That thing I don't know. Though, indeed, it sounds OK and some natives even use "That I don't know" in the same context.
Also, what about That one I don't know? Sounds like native English to my non-native ears :)
- That one I don't know.
- That thing I don't know.
Not (really) sure about that (one). I don't (really) know about that. Can't say about that (one) - are among those I've heard from natives.
...a helpful reference I found on this. Still I think the question is valid. Should I say "I don't know" or "That I don't know"?