Portugal international Nani has not played since early December after sustaining a hamstring injury.
"Nani has had a bad hamstring injury. He's getting closer now but I think it will be another month until he will be about ready to play," Moyes told the club website (www.manutd.com).
England midfielder Carrick missed Tuesday's league win over Cardiff City at Old Trafford with an ankle problem.
"Carrick is improving with his ankle and has got a good chance of being in the squad," Moyes added.
"He's improving and has done some training. We'll just check to see if he can twist and turn correctly before we make a decision."
United are seventh in the standings, 13 points behind leaders Manchester City.
(Editing by Justin Palmer)
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