Danny Sullivan from Google said Google is "looking at" providing a mechanism to block pages or subsections of your site from being displayed in Google Discover. This comes off the controversy that there are new manual actions for Discover and Google News but no way to control if you show in Discover.
Here is the post on Twitter where I am getting this information from:
There's no way to do that now. It's something we are looking at.
— Danny Sullivan (@dannysullivan) February 18, 2021
It would be nice to have some sort of control of where your content can not be showed in Google. You can block it from search and other areas but right now, if you are in Google Search, you can be found in Google Discover.
So it looks like Google may work on some new mechanism for us to block our content from showing in Google Discover.
Forum discussion at Twitter.