Zaha has yet to make a single Premier League appearance for United since joining the club in a £12million deal from Crystal Palace this summer.
"Wilf has not appeared," United boss David Moyes said. "We have not felt we have had the opportunity.
"I want Wilf to get used to what happens here. The competition is hard. It is just impossible to get all these players a game at the one time. You can only ever play eleven.
"But it is important Wilf gets to see the level of the training here, the level of the players and the quality they have got. He is getting better, which we are pleased about."
The Daily Telegraph reports that the England international will seek a loan move away from United in January.
Newcastle, West ham and Fulham are all interested in signing Zaha on loan in January.