Zaha linked up with United during the close season after signing from Crystal Palace in a deal worth up to £15m, but he has still to make his Premier League debut.
The 20-year-old could be handed a start against Norwich City in the League Cup later on Tuesday, but Moyes has admitted that he may be loaned out during the January transfer window.
"I just don't think we have had the right opportunity to get him on as much as would have liked," Moyes told United's official website.
"We don't want to put him in too quickly. We want to make it the right time. I've said I would look at [a loan] in January as I wanted to have him here for six months to see how we work.
"I told him we would try to get him minutes, but the competition in the wide areas we have with Nani, Antonio Valencia, Ashley Young, Adnan Januzaj and even Shinji Kagawa playing off the side means we are as strong there as anywhere.
"It's not that Wilf has done anything wrong, it's just that we have big competition and we have to try to make sure he gets some playing time.
"Unfortunately we haven't done that with Wilf and, if it's still the case in January, we would look at it. But he is very much in my plans and in my thoughts all the time."