This could go either way. By letting each party know about the other, one of them may make a move thinking that they may miss out if they don't, or both could make a move and you could have a bidding war on your hands.
The other thing that could happen is that each party decides that they do not want to get into a bidding war and one or both back away leaving you with no interested parties.
I am guessing that you are offering your property For Sale By Owner? Regardless, if the REALTOR's buyer had a continuing interest, it would have been made known to you, as the REALTOR would have came back to you with more questions and dialogue about your property on behalf of that buyer. As far as the private buyer? You probably have no idea if they can even buy your property, or any property, for that matter. If it were me in this situation, I probably would not say anything to either party unless asked. Maybe something like "We have some parties looking at it, but who knows? Whoever gets here the firstest with the mostest!"
Jim Dvorovy, REALTOR
Cutler Real Estate
203 Applegrove NW
N. Canton, Oh 44720