Zaha, who has won 12 caps for England Under-21s and two for the senior side, has yet to make his Barclays Premier League debut for the Red Devils and has been linked with a loan move away in the January transfer window.
He could line up against Norwich in the Capital One Cup on Tuesday night, though, and Moyes is keen to see him in action.
"I just don't think we have had the right opportunity to get him on as much as would have liked," Moyes told the United 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."
Also seeking to play his way into the first-team picture is midfielder Darren Fletcher, who made his competitive return on Monday in an under-21 game against Fulham.
The 29-year-old Scotland international has played just 13 games since announcing he was taking an extended break from football in November 2011 after being diagnosed with ulcerative colitis.
He has since undergone several operations - the last of which took place in January - and been put on a strict dietary regime in a bid to correct his stomach condition and allow him to resume playing duties.
Fletcher was finally given the all-clear to return to training last week and on Monday night took the first steps towards a first-team comeback by playing 67 minutes of the 2-2 draw.
"I've been training for a few weeks now and the next progression is to get some match time. I enjoyed it," he told MUTV.
"The plan was to get to half-time and see how I felt. Then get to 60 minutes and take it from there and, although I felt I could have gone on a bit longer, the plan was not to play more than that so I'm better sticking to the plan and not upsetting the sports science lads."
Source: PA
Source: PA