Cannot install MS Office updates

According to End-user update notifications for Office 365 ProPlus:

After updates are downloaded to the computer that is running Office 365 ProPlus, Office attempts to apply the updates. If, after four days, the updates still aren't applied, a message appears in the notification area in Windows, telling the user that updates are available.

The message disappears in a few seconds, but the Office icon stays visible in the notification area. If the user clicks the message, Office tries to apply the updates. If any Office programs are currently being used, they must be closed.

If, after six days, the updates still aren't applied, a message appears in any newly opened Office document, reminding the user that updates are available.

Users can choose Update now to apply the updates. The user is then prompted to close all open Office programs. After the updates are applied, the message disappears.

Users also see notifications if they go to File > Account in an Office program. The Office Updates section turns yellow if updates are ready to be applied.

Here is a similar thread in TechNet Office Forum for your reference: Office updates are available. It's just a notification. You can manually apply update your Office 365 in any Office application.