Imac shows I need update but will not update Imac os bigsur version 11.6.7

I've had better luck from the Safe Mode because I evidently have some 3rd party software that interferes with the installation so try the following:

#1 - boot into Safe Mode according to Start up your Mac in safe mode - Apple Support.

NOTE: Safe Mode boot can take up to 3-5 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

#2 - go to the System/Software Update preference pane and begin the download.

#3 - run the installer from the Safe Mode.

Hi,

Using this Apple Support article as a guide, About System Information on your Mac - Apple Support, please let us know what year your Mac is.

Jack

You should be able to run the highest version of Big Sur 11.6.8. Are you checking for updates using System Preferences > Software Update?

Update macOS on Mac - Apple Support