Managing personal Outlook.com account settings, security, and privacy
Hi! Is the Outlook email address already added as an alias to the Microsoft account that uses the Gmail address, or did you create a separate Microsoft account using that Outlook email address and now want to add it to the Microsoft account that uses Gmail?
If the Outlook email address is currently associated with a different Microsoft account, it cannot be added to another Microsoft account. An email address can only be used with one Microsoft account at a time. In that case, you would need to sign in to https://account.live.com/names/manage and create a new Outlook.com email address for the Microsoft account that uses Gmail, since an Outlook email address that has already been used for one Microsoft account cannot be reused on a second one.