OS X could not be reinstalled, saying No packages were eligible for install

Did you maybe use Firefox to get that AppStore link, if so try Safari...

Don't use FireFox for this link, it’ll offer strange erroneous errors…

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

If you get a corrupted message...

Naw, not damaged, it's just that you have an old copy already in Applications, there are 2 cures...

Disconnect from the Internet & set the Date back to 2014, then you can run the Install MacsOS Mohave App in Applications, so expired Certificates are not expired.

Or... trash the Install MacsOS Mojave.app in Applications, empty trash & restart, then a new copy of a more recent version can be downloaded..

Hi, Jeffers259.

To start, you missed the part where you tell us what model year your iMac is and what OS you were trying to upgrade from and to. To find the details about your Mac model, click the Apple  icon at the top left of your screen and choose About This Mac.

These Mac models are compatible with macOS 10.14 Mojave:

• MacBook (Early 2015 or newer)

• MacBook Air (Mid 2012 or newer)

• MacBook Pro (Mid 2012 or newer)

• Mac mini (Late 2012 or newer)

• iMac (Late 2012 or newer)

• iMac Pro (2017)

• Mac Pro (Late 2013; Mid 2010 and Mid 2012 models with a

   recommended Metal-capable graphics cards.

These Mac models are compatible with macOS 10.15 Catalina:

• MacBook (Early 2015 or newer)

• MacBook Air (Mid 2012 or newer)

• MacBook Pro (Mid 2012 or newer)

• Mac mini (Late 2012 or newer)

• iMac (Late 2012 or newer)

• iMac Pro (2017)

• Mac Pro (Late 2013 or newer)

These Mac models are compatible with macOS 11 Big Sur :

MacBook (2015 or later)

MacBook Air (2013 or later)

MacBook Pro (Late 2013 or later)

Mac mini (2014 or later)

iMac (2014 or later)

iMac Pro (2017 or later)

Mac Pro (2013 or later)

This sounds more like you are trying to reinstall the OS from the Apple Recovery Servers rather than simply upgrading the OS.

The certificates for several of Apples OS's expired in October 2019, Apple haven’t bothered getting these updated on 

their Recovery Servers with valid certificates. 

This may be the problem you are experiencing. 

Try this workaround, we are going to set the time and date on your mac to a date previous to the expiry date of the certificates.

Connect your mac to your router via cable, not WiFi

Boot to your Recovery HD, click on Utilities in the menubar select Terminal.

Make sure WiFi is switched off, it can reset the date back to today.

Enter a new date, for example or just copy and paste

sudo date -u 011421002017

press Return

enter your password

press Return

If Terminal returns an error saying sudo : command not found, then try again without sudo.

just enter 

date -u 011421002017

press Return

You won't be prompted for a Password if you did not need to use sudo

Once the date has changed you can quit Terminal.

Now try downloading the OS.

Click on Install OS X, press Continue.

If this works then when the OS is installed and booted up you can Open System Preferences> Date & Time

and reset the time back to today.