United recently landed in Sydney as part of their summer tour of East Asia and Australia.
"Well, there is [fear of injury] because you always pick up one or two knocks or niggles," Moyes told reporters. "My preference was to come with a smaller squad because I wanted to make sure I got as many players playing minutes, and I didn't end up bringing a lot of players who ended up travelling half way around the world for three weeks and ended up not playing enough games.
"So I wanted to focus on getting as many players as much time as I could. I think it's always good once you get the first one under your belt, you feel much better by it.
"Ashley Young has started some training, Chris Smalling started some light training, Nemanja as well has started, so we do know that if we need them we can probably call on them."