The 5e Unearthed Arcana *[Races of Eberron][1]* (v1.1) says:
>Although they are constructs, they have
much in common with living creatures, including emotions
and social bonds, and **perhaps even souls.**

This last part troubles me however. 

**Do warforged canonically have souls?**


  [1]: https://media.wizards.com/2015/downloads/dnd/UA_Eberron_v1.1.pdf