The Red Devils have already lost 6-1 at Old Trafford to Roberto Mancini's men this season, and they come into this fixture having fallen to two successive losses in the Premier League - against Blackburn Rovers and Newcastle United.
Another defeat by City, this time at the Etihad Stadium, would knock United out of the FA Cup at the earliest stage, giving further ammunition to their critics following the early exit from the Champions League.
"Apart from the local pride at stake, with both teams battling it out for the title - even though Tottenham refuse to let them have it all their own way - the result could have a big psychological impact on the rest of the season," Neville wrote in his column for The Mail on Sunday.
"It's not so much going out of the FA Cup which will disappoint either team - though that would be bad enough - it will be that sense of losing the initiative to their closest rivals.
"And, having lost 6-1 to City at Old Trafford, and having now lost their last two games, Manchester United have to react.
"Everyone will be looking at them.
"Two defeats is perceived to be a crisis at United and that feeling would only grow if they were to lose a third to City."
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