Download update before asking for restart
You might need to check the boxes "Check for updates" and "Automatically download updates when available" for the download. Also, Check firewall options for allowing connections if denied.

https://forums.macrumors.com/threads/where-are-downloaded-software-updates-stored.1629444/ and as I too verified, updates are located in Library/Updates before install.  You can verify if it is available for install or not.