The former Crystal Palace winger has kicked off his United career this past week.
"It was a bit nerve-wracking at first, coming in and seeing all these players that I've watched over the years," Zaha admitted to MUTV. "But everyone seems all right so I'm settling in okay.
"I'm speechless really, I just never thought I'd have the chance to play with the likes of Rooney and to actually be sitting next to Giggs in the changing room. It's just a dream really."