The Red Devils take on league leaders Arsenal on Sunday at Old Trafford, and Moyes said that he believes Arsenal will remain in the title race for the whole season.
"We want to keep the results going and keep improving," Moyes told the club's official Twitter feed. "Hopefully we can keep that momentum going.
"[Arsenal] have had the benefit of continuity. They have the same chance to win the title as we all do. Their form has been good."