CyanogenMod is already running on the Samsung Galaxy Note 3 as can be seen from the above pciture shared by Cyanogen on Google+. Of course this has to be either the international version or the T-Mobile version, AT&T and Verizon users need to wait for a safestrap kind of recovery or a bootloader hack.
Anyways, the build has not yet been released but once it is posted rest assured we here at TeamAFN will let you know about the same.