The 20-year-old, who signed for the Red Devils in January, will begin life with his new teammates following his switch from Crystal Palace.
"He will travel with us on the tour," Moyes told talkSPORT. "He has only been with us for two days but I will take him away, see how he goes and have a look. This club has a great record of putting young players in the team. Hopefully Wilfried can be one of them."
There were reports that Zaha may return to Selhurst Park on loan, but it is believed that the England Under-21 international will fight for his place at United.