Download update before asking for restart
Solution 1:
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.