The Belgium international has not featured since the 1-0 home defeat against his former club Everton early last month after undergoing surgery on his wrist.
Fellaini has also been troubled by a back problem, but Moyes has admitted that the 26-year-old is closing in on a return.
Combative midfielder Fellaini will have his cast removed on Monday and will then be looking to stake his claim for a place in the United starting line-up.
"Hopefully next week we'll get him back." Moyes told MUTV.
Fellaini has not reproduced the sort of form that he showed for Everton at the start of his United career, so he will be eager to make an impact when he returns to the first team.
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