The result of the contest could play a huge part in whether or not the Canaries retain their Premier League status.
At the moment, Norwich are 19th in the table, two points off safety, with three games left to play.
Neil's side also have one game more to play than Newcastle United, who currently occupy the survival spot.
"Anytime you are going into big game it becomes your biggest game, anything you have done in your past no-one really cares about anymore, it doesn't become important," the Daily Mail quotes Neil as saying.
"So this is certainly the biggest game of our lives at the moment because it is the most relevant for us and is going to shape the future for us going forward."
Manchester United have something to play for themselves as they are four points off a Champions League spot.