Fifth-placed United moved to within a point of City after their 2-0 win at Burnley on 23 April and could overtake their rivals with victory at the Etihad Stadium in midweek.
City lost the FA Cup semi-final 2-1 against Arsenal at Wembley on 23 April, meaning Pep Guardiola will end a season without a trophy for the first time in his managerial career.
Former United defender Neville said the Manchester derby had taken on "incredible significance" after the weekend results.
"If United are to win, they could go above City. This month is absolutely critical. It's a huge test on Thursday," he told Sky Sports.
"City are a really good side and can pick you apart. It will be interesting to see what [United manager] Jose [Mourinho] does.
"He usually has a tactic going into a big game and it will be interesting to see how he adapts and how he changes it."
United lost the reverse fixture against City by a 2-1 scoreline at Old Trafford in September, with Kevin De Bruyne and Kelechi Iheanacho scoring for the visitors.
However, the Red Devils avenged that loss a month later with a 1-0 win over their bitter rivals in the EFL Cup round of 16 at Old Trafford.
Neville said he was impressed with how United coped with the absence of long-term injury victims Zlatan Ibrahimovic and Marcos Rojo at Burnley.
"From a Manchester United point of view, the two performances in the league are probably the best I've seen them home and away. In terms of professionalism definitely, they were really comfortable and managed the game well," he stated.
"And the distraction of the bad injuries to Rojo and Ibrahimovic. If before the game you told me it would unfold like that, I would have been surprised."