Van Persie was ruled out for up to six weeks after spraining his knee during the closing stages of United's 3-0 triumph over Olympiacos in their Champions League knockout tie last month.
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But Moyes told reporters on Friday that the 30-year-old is progressing well in his recovery.
"Robin is over in Holland having treatment and we get a daily update of exactly how he is," he said. "He's getting better.
"He's doing all of his recovery and rehab back there. He's coming on, as far as we know.
"I was told four to six weeks by the doctors and there hasn't been any reason to tell me any more or any less time.
"We will monitor that. My hope was that we would get him back before the end of the season, that's for sure.
"The big thing is we'll be medically led. We won't push. If it's not right, we certainly would not bring him back sooner. We will totally be led by the medical team and Robin.
"Robin is a good judge of how his own body feels. It's part of how we've tried to deal with Robin through the season and giving him the understanding that he tells us how he feels. He'll be the first one to tell us how he is."