Don't know why you are getting that message, are you using Safari to connect to the AppStore, Firefox we know does not work.
Open Safari and click on this link,
How to upgrade to macOS Catalina – Apple Support
Go to Section 4 and click on Get macOS Catalina.
This will redirect you to the App Store
The Catalina page should say Get or Download.
In theory it is, according to Apple to upgrade to Catalina from Mavericks, in practice a lot of people face the installer getting frozen as it tries to convert the HFS+ file system to the new APFS file system.
So my recommendation would be to do an interim upgrade to macOS High Sierra.
Again open Safari and click on this link.
How to upgrade to macOS High Sierra - Apple Support
Before upgrading make a full back up of your Mac.
Check that third party apps you use have updates available for the new OS.
https://roaringapps.com
Check that your printers/ scanners etc have updated drivers and software available for the new OS.
Connect your mac to your router via cable rather than rely on WiFi.
Do not use your mac while it is downloading
and do not use any other devices that share the same internet connection.
If the App Store says ‘Open’ then it is detecting a previous download of the install app
go to the Applications folder locate Install macOS ******.app.
Move it to the Trash, empty the Trash.
Restart, click on the link again, the App Store should say ‘Get' or 'Download'.
If you are considering upgrading to Catalina be warned that it does not support 32bit apps.
Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,
some updates may be free, some may be paid. Use this app to discover which apps you have
are 32bit, https://www.stclairsoft.com/Go64/. Once the list has been created you can then
contact the developers of the apps to see if they provide 64bit updates.