Over recent weeks, the Blues have struggled to adapt to their new home, with Everton's last victory at the Hill Dickinson was in December against Nottingham Forest.
The 1878s, a fan group that performs displays before matches, are planning another one for the game on Monday night, which has the manager's backing.
"It will be hugely helpful, and it will be hugely appreciated if they do, because anything we can get at the moment to help. At home, it's been difficult for whatever reason that may be."
"The people who make football clubs are the supporters. Inside the stadium, they are the ones who make a big difference.
And if they can help make a difference on Monday night, that'll be very much appreciated."
Moyes has set the task for his side to do the double over Manchester United for the first time since the 2013/14 season.
Last time out, the Blues won 1-0 despite being down to ten men, thanks to a goal from Kiernan Dewsbury-Hall. Idrissa Gueye got sent off following an incident with Michael Keane.
"We've got a really good goal and did well enough to hang on to it. It was a really important three points, and these three points coming up are important again."
Everton did the double over Nottingham Forest and Fulham, and will hope to add Manchester United to that list.
Despite the inconsistencies the Blues have shown over the course of the season, Moyes is adamant that Everton won't be a team fighting relegation as they have in the last couple of years, and highlights what the next steps are for his team.
"I think the challenge now is, can we change mentality, can we change the whole direction we’re going in.
"We're not going to be that team anymore; we're not planning to be a team that's fighting relegation.
"We're a team that's planning to try and challenge the teams in Europe, and to do that, we’re going to have to win some big games in the run-in."