Fletcher on the road back
But Moyes insists the Scotland international will not be rushed as he eases back into a routine of training and playing.
Fletcher made his first appearance for United at any level in 10 months on Monday as he played 67 minutes for the under-21s against Fulham at Salford.
The 29-year-old has featured little since being diagnosed with ulcerative colitis in December 2011.
He did return to make 10 appearances for United, as well as three for Scotland, last season but his comeback was put on hold as he underwent surgery in January.
Moyes said: "It is great to get Darren back.
"It was the first time he pulled on a jersey in a competitive reserve league game (since the operation) and we're really pleased.
"We will bring him along, his training is coming along well, but we don't want to do anything that might give him a setback.
"It is a sort of steady, slow grind for him just now.
"But we are pleased and hope to involve him in the upcoming reserve games in the weeks to come, if he continues to do as well as he is doing now."
Moyes has sensed a strong desire within the game to see Fletcher, a former United trainee, back in action soon.
Fletcher last played for the first team on Boxing Day last year.
Moyes said: "I think with the nature of his illness, everyone should be hoping he comes back.
"It is the sort of thing that, whatever walk of life you are in, you want to see people make recoveries from illness or other things that are wrong with them.
"Darren has shown that with the right medical treatment, by looking after yourself and doing the right training you can get back to where you were."
They could now both feature against Fulham at Craven Cottage in the Barclays Premier League this weekend.
Moyes said: "I think they are both very close. They played against Premier League opposition in midweek, they both played 90 minutes.
"I can't see any reason why they wouldn't be ready to be selected or be involved."
England international Danny Welbeck will not be involved in London as he continues his recovery from a knee problem.
Moyes said: "Danny Welbeck has had a bit of fluid on his knee.
"He has trained a few days this week and he is certainly getting much closer to match fitness but he will not travel this weekend."