The duo have been sidelined with Achilles and thigh problems respectively, with Van Persie featuring just twice in December.
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Yet Moyes is hoping to see the pair take some part in United’s upcoming games, telling reporters: "There are always miracles at Christmas time so let's hope there could be one for Robin van Persie or Michael Carrick.”
Moyes also revealed that Marouane Fellaini will be sidelined for six weeks following wrist surgery, as reported by Goal on Monday morning.
"He had his operation on Saturday morning," he added. "We just couldn't get him recovered from his back injury.
“We thought his back would be okay after 10 days but it wasn't getting any better, so we made a quick decision to get his wrist operated on, to get it done quickly. We think it will be six weeks but there's a chance it will be before that.
"His back problem was just going to take time. It was a muscle injury, which wasn't healing so it was maybe going to take longer than expected. That's why we decided to get the wrist done.”
The Belgian has featured intermittently for the Red Devils since signing from Everton for £27.5 million and has suffered problems with his wrist since the beginning of the season.
"He doesn't feel 100 per cent fit because of the wrist," Moyes continued. "I asked him to see over the Christmas period. He got the back injury against Everton and since then he's never really been right, but we thought we might have got him back in a couple of weeks.
"He tried it and it wasn't right, so we thought the best idea was to move on, have the surgery on his wrist and give his back a chance to get well too."