The England international, replaced by Jay Rodriguez in Roy Hodgson's latest squad, will miss the visit of the top-of-the-table Gunners with a knee injury
The 22-year-old missed victory away to Fulham with a knee injury and, despite returning to training ahead of their midweek trip to Real Sociedad, was also omitted from the midweek Champions League squad.
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"We want to keep the results going and keep improving," he said in a press conference. "Hopefully we can keep that momentum going.
"Arsenal are coming to play the champions. They're top and will come here in good spirits but we want to put on a good show.
"They've had the benefit of continuity. They have the same chance to win the title as we all do. Their form has been good."
However Moyes, who could secure his club's sixth consecutive home victory in the league against table-toppers Arsenal on Sunday, admitted is was another "tough" fixture handed to him at the start of his reign.
He added: "For a new manager coming here it's a tough set of fixtures but if you're Manchester United, you're used to it."