Morpheus was aware that Neo was not the fist "One", in fact he specifically mentions this as part of Neo's induction, I haven't seen the first movie in a while but off the top of my head he said something like,"there was a man born inside who had the ability to change whatever he wanted, to remake the Matrix as he saw fit, it was he that freed the first of us". So from the beginning it was understood that Neo had at least one predecessor. Unfortunately this creates way more questions than it answers. Neo's question throughout the series seems to be "I wish I knew what it is I'm supposed to do", so the real question is, what did Neo think his predecessor achieved or failed to achieve that made it relevant at all to have another One? Just another edit here, it seems then that although Neo was aware of at least one predecessor, he was not aware of previous iterations of the Matrix, this is why he says to the Architect "either no one told me, or no one knows", which is said by both the current Neo and what seems to be a recording of his predecessor on one of the monitors, to which the Architect replies "precisely". Also, when Neo asks the Architect "why am I here", the Architect gives him an explanation of where he comes from but not why he is in fact there, when Neo says "you haven't answered my question", the Architect smiles and says "quite right" but also says "interesting, that was quicker than the others", to which the predecessors on the monitors are surprised to hear that there were others, but the current Neo is not, he seems to be the only One that knows he is not the first, however it must also be that each "One's" answer was quicker than the last.