The Netherlands international, who has been struggling with groin and toe injuries, has been absent since notching the winner against former club Arsenal in a 1-0 triumph at Old Trafford on November 10.
Van Persie - who has seven Premier League goals to his name this season - travelled with the squad for their 2-2 draw at Tottenham on Sunday but was deemed not fit enough to join the matchday squad.
But, speaking ahead of the home match against his former side, Moyes confirmed the 30-year-old could return to the fold.
"Robin is okay," he said. "He has a chance of playing."
The fixture with Everton marks the first time Moyes will take charge of United against the club where he enjoyed an 11-year spell as manager.
And the Scot admitted he is not sure what sort of reception he will receive from the travelling support, while also praising the job done at Goodison Park by successor Roberto Martinez.
He added: "I had a great time at Everton, they were fabulous to me. Overall we had a (good) level of consistency.
"I think it will be a mixed reception tomorrow night. The Everton fans understand their football and I think they'll understand I brought in a lot of good players there.
"He (Martinez) is doing a very good job. He has very good players there. I always told them they could play without a manager because they are very well organised. But Roberto is doing a really good job keeping it going."
United have recorded 2-2 draws in their last two Premier League matches at Cardiff City and Tottenham, and are on a seven-match unbeaten run in the top flight.
And Moyes is keen for the reigning champions to build on that consistency.
"The job is to keep it going, keep winning and keep on a good run of form," he commented.
"We've done that but as I've repeated myself many times we let in a late goal at Cardiff which turned what would have been a really good week into one that wasn't quite as good as we would have liked."
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