David Chalmers (who initiated the term "hard problem of consciousness") has suggested that finding the neural correlate of consciousness is part of the "easy problem":
"At the end of the day, the same criticism applies to any purely physical account of consciousness. For any physical process we specify there will be an unanswered question: Why should this process give rise to experience? Given any such process, it is conceptually coherent that it could be instantiated in the absence of experience. It follows that no mere account of the physical process will tell us why experience arises. The emergence of experience goes beyond what can be derived from physical theory."
In the same paper he goes on to describe a possible non-reductive explanation in which consciousness is a fundamental property of the universe.