Both could be correct. I would remember = my brain would contain the knowledge now. I would have remembered = my brain would have stored the knowledge at the time you told me (and, as a consequence, my brain would contain that knowledge now).

I have to agree with Claire. If you're talking about remembering in the present moment (I don't understand the comment that says we can't remember right now), 1 is correct. 2 would be correct if the act of remembering is in the past.

I would say 2. The act of having remembered is not "right now", but in the past. So "would have" sounds more natural in my opinion!

*Which The correct is 2.