One of the attributes of that Supreme Consciousnessness is that it is NOT an object., but the ever-knowing subject.

Adrushya - is one of the 1000 names given to that Brahman in Vishnu Sahasranamam. It means that one who cannot be realized completely by anyone. 

Drik-Drishya Viveka a famous book that distinguishes between subject & object. Adrushya and Drishya which are opposites basically mean that whatever we see /experience is drushya (drishya) and what remains in this Universe after ALL we experience is Adrushya, which is Brahman.

It is a nice way of explaining that Universe = Consciousness + Matter. Matter is object and Consciousness is subject.

The Consciousness is 'I' or Atma.