You can send an offer to watchers on your buy it now items only, not on your auctions.
On your selling page, at the top, there will be a big and bold
Send offer to buyers
and a list of eligible items.
Sending offers is anonymous as you don't know the watchers' names.
"There are two ways to be fooled. One is to believe what isn't true; the other is to refuse to believe what is true.”
Søren Kierkegaard, Danish philosopher (1813 - 1855)