It has been claimed in some newspapers that Zaha had stormed off during a United training session after learning that a potential loan move had been blocked.
Cardiff City are understood to be in pole position to land the England winger, who is very much on the fringes of the first team under Moyes.
Moyes insists he is looking to get Zaha out on loan, but says injuries to Nani and Ashley Young mean that he cannot allow him to leave at the moment.
"I have told him that if I can't get him the games I will put him out on loan," Moyes told the Independent.
"But he can't go out while we have Ashley Young and Nani injured and I would be surprised if anyone thought there was a possibility [of those two returning before the transfer window shuts]."
Moyes insisted that there was no bust-up in training and said: "I had 30 seconds chat on the training pitch and we were talking away. So there was nothing like that."