Is there consciouness when a person is sleeping and not dreaming? According to 

Consciouness


  Consciousness is the state or quality of awareness or of being aware
  of an external object or something within oneself.


I suppose dreaming qualifies as "being aware of an external object or something within oneself". But what about sleeping without dreaming. Is there supposedly consciousness in that state?
According to Giulio Tononi,"consciousness is what goes away when you fall into a dreamless sleep,” he explained that  "once a person goes into dreamless sleep, there is no experience, no perception of surroundings or the environment; there are no memories of the past or the future or even the present. It is thus at this point that everything disappears, which corresponds to consciousness “going away.”" [1]
You can look up his integrated information theory of consciousness [2]


Tononi G, Edelman GM: Consciousness and complexity. Science. 1998, 282 (5395): 1846-1851. 10.1126/science.282.5395.1846.
Tononi, G. (2011). The integrated information theory of consciousness: an updated account. Archives italiennes de biologie, 150(2/3), 56-90.