Sending, receiving, and organizing email in Outlook.com
Hi
This usually happens when Microsoft is asking you to add or verify a Microsoft account alias. A Gmail address can only be added if it is not already used as an alias or sign-in address on another Microsoft account.
Please try adding a new Outlook.com alias instead of Gmail from this page: https://account.live.com/names/manage
Choose “Add email” → “Create a new email address and add it as an alias”, then verify it and try signing in again. Microsoft’s alias guide is here: https://support.microsoft.com/account-billing/how-to-add-an-email-address-or-phone-number-to-your-microsoft-account
If you still cannot sign in, use Microsoft’s sign-in helper here: https://support.microsoft.com/account-billing/can-t-sign-in-to-your-microsoft-account
Please do not delete your current primary alias unless you are fully sure, because removed Microsoft aliases may not be recoverable.