Zaha was a second-half substitute in Moyes's first game as manager of the Red Devils as they fell to a 1-0 defeat to Singha All Star XI in their opening pre-season match.
"Wilfried did well," Moyes told reporters. "He gave us a little bit of something different.
"We have brought him here to give him a chance. It is the first time I have worked with him and had a chance to see him up close.
"He will certainly be part of the squad and we will see where we can fit him in as often as we can."
Zaha scored eight goals for Palace last season as he fired them into the Premier League.