There is currently no out of the box solution to what you've been asking for. FNMS has more of a pull approach. In some menus you'll find an "Events" submenu. That would usually be the way to get the data. Whoever is responsible for this process, could set up such report as one of their browser start page, to have a glance at it at least once a day.
For FNMS On-prem: You could use 3rd party tools to access the FNMS databases and do your own reporting an emailing. SQL Server Reporting Services (SSRS) would be an option. Or perhaps, some PowerShell scripting?
This has been kind of requested here: https://community.flexera.com/t5/FlexNet-Manager-Blog/Have-an-idea-for-changing-FlexNet-Manager-The-...
Vote it up, if you like.