I get Facebook friend requests where I'm not sure I know the person... but maybe I do.

Is there a feature that I can turn on so that I can reply to the request (but not accept or decline) asking the person how they know me?

It's a pain in the butt to go to the person's profile and message them. It would be nice to just click on a button that says "Reply without accepting or denying".

Is that possible?

Thanks!

Nope. You can Hide it, then you can Delete Request or Confirm.
To message the person it's just a matter of clickling on their name and sending a message from there; it's actually a good exercise to view their profile, might give you a better idea of who they are.

Thanks. I was thinking that was the case... but hoping there was some feature that I did not have turned on.