Upgrade direct install software from App Store

I have Microsoft Office installed on my Macbook Pro which I downloaded from Microsoft's website. I see it is also available on App Store. Is it possible that the future upgrades to software can be shown within the App Store, although I downloaded and installed it directly from elsewhere?

This will prevent me uninstalling the setup completely and downloading and installing a new one from the App Store.

No, unfortunately this is not possible.

You can only update software within the App Store that was download directly from the App Store.

Just delete the apps. All your documents and preferences and licensing remain. Then download the App Store versions. We do this all the time when we want Apple to assist with the updates instead of Microsoft updates. Each is excellent in some cases, so choose how you like best and change is as your needs or preferences change.

The apps from the store have signatures that control updates, so you can’t tack that on later, in general or in specific for Office.