Microsoft persist year after year in saying their new Mac (insert your choice of Microsoft app here) piece of software is now equal to the Windows version and yet when you actually check this turns out to be a lie each time. So Outlook 2016 for Mac is far, far less capable than Outlook 2016 for Windows. See https://technet.microsoft.com/en-us/library/jj984198(v=office.16).aspx
However even that article does not really address your particular issue. As you have found Outlook 2016 does not support syncing via iTunes on a Mac, Microsoft expect you to be using a Microsoft Exchange server. If your email account is via an Exchange server then your Outlook 2016 for Mac will sync contacts to your server account, and your iPhone will also sync contacts to and from the same Exchange account.
If you don't have an Exchange account then there is little to no justification for using Outlook on a Mac at all. If you must be a masochist and do so then your only option is to export your contacts from Outlook 2016 and then import them in to Apple's Contacts application. You can then either sync Apple's Contacts application via iTunes or set up a free iCloud account or a free Carddav account (e.g. Google Mail) and then have the Contacts application and iPhone both sync their contacts via that free account.
Just in case anyone else tries going down the wrong path, Outlook 2016 for Mac does not support Carddav accounts, nor are there any plugins to add this to Outlook 2016 for Mac.
There is one final scenario that is a solution for some. Kerio make a mail server called Kerio Connect, this supports EWS (Exchange Web Services) as used by Apple Mail , Apple Contacts, Apple Calendar and Outlook 2016 for Mac, it also supports Carddav as used by Apple Contacts and iPhone, and it also supports EAS (Exchange Active Sync) as used by iPhone. It does not support MAPI as used by Outlook 2016 for Windows. If you do have a Kerio Connect server then you can sync contacts from Outlook 2016 for Mac to it, and also sync your iPhone to them same Kerio Connect account. Kerio Connect is not free.