Shore took over for Jeff Cassar, who was fired on Monday, just three games into the season. Real Salt Lake (0-2-1) is averaging 2.3 shots on target per game, the third-lowest total in the league, and has scored just once this season.
Shore, the club's former Director of Goalkeeping, will be without star midfielder and team captain Kyle Beckerman, who is suspended for the match. Beckerman picked up two yellow cards last week against the Los Angeles Galaxy, earning the automatic suspension.
"We're focused on New York," Beckerman said. "I felt for Jeff (Cassar), he's a good friend of mine. I know how much he cares for this club. It's his team. We're going to continue to try and get a win to get the season to where we want it. There's really no reason to panic."
The Red Bulls (2-1) will also be without their captain Sacha Kljestan, who was called up to the U.S. men's national team this week by coach Bruce Arena.
Despite having its 18-match unbeaten streak in the MLS regular season snapped by Seattle on Sunday, New York looks to continue its strong play at home. The Red Bulls have the best home record in the league at 76-24-18 (246 points) since Red Bull Arena opened in 2010.
Under head coach Jesse Marsch, the Red Bulls own an impressive 28-6-4 home record.
With a goal last week against Seattle, Red Bulls' striker Bradley Wright-Phillips became the third fastest player to reach 70 goals in MLS history, behind Roy Lassiter (104 games) and Robbie Keane (106).
Wright-Phillips earned his 70th in his 110th MLS appearance.
Red Bulls goalkeeper Luis Robles extended his MLS record last weekend with his 143nd consecutive MLS regular season start.
"Because of the new coach and the situation that they (Real Salt Lake) are in, there's a lot that these players have to prove and I think they are going to use this game exactly to do that."