Outlook does not use JIRA for authentication so the two won't link up in that manner as it would if you had an external directory added to JIRA. If you're using Active Directory and JIRA you may want to take a look at the Microsoft article titled Syncronizing your directory with Office 365 is easy to see if a solution such as the one proposed there works for you.
If you mean Office 365 and Jira server, there's actually a plugin for this: Office 365 Directory Connector for Crowd (ODCC)
Please note that you will need Crowd in between Jira and Office 365.
(Disclaimer: I work for the vendor of this plugin)
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