No Updates Availible?

Back up your data, check your applications for compatibility, click here, and depending on which Mac mini model you have, then on the download link for Mojave, Catalina, Big Sur, or Monterey; it needs to be at least a 2012 one to run a higher OS. If you get a Mac App Store preview page, change the https at the beginning of its address to macappstore.

Catalina and newer won't run 32-bit software; download and use Go64 to scan for it. To look other programs up, click here.

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iOS is used on iPhone or iPAds

macOS is used on Apple Computer

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence.

Computer Qualify for the Monterey upgrade

macOS Big Sur 11 hardware requirements

macOS Catalina 10.15 hardware requirements

macOS Mojave 10.14 hardware requirements

Caution - jumping over all the newer versions and directly to Big Sur  / Monterey on Qualifying computers is Technically possible - there are those who have attempted and were successful.

Then there are those who attempted and had less than good results.

If this is a Production or Mission Critical Set-up - a more prudent and measure approach is suggested. 

The above is from observations on the Apple Support Community Forums and IMHO

Tips Big Sir Upgrade Released Nov 2020

Tips Monterey Upgrade  Released Oct 25, 2021

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

What year model is your Mac mini?

see > Identify your Mac mini model - Apple Support

To check the hardware requirements for macOS versions.

have a look at > How to get old versions of macOS - Apple Support