New Zealander Smith was linked with the specialist backs role and is considered one of the world's top attacking coaches.
However, the 54-year-old confirmed that he has not been contacted by England, saying: "I'm really happy here [at my coaching role with Waikato Chiefs] at the moment. I'm close to family and enjoying the game.
"The NZRU have been great to me and I'm not desperate to coach overseas, although one day I'd like to be in the Test arena again."
London Irish's Mike Catt and Clermont Auvergne's Alex King have now emerged as potential candidates for the role in Stuart Lancaster's coaching staff.