The Belgian midfielder required surgery on a serious wrist problem and has not been available since the defeat to his former club Everton in early December.
"I think we had nine players out [last weekend against Swansea City]," manager David Moyes told MUTV in an exclusive interview.
"Fellaini will have the cast taken off his hand on Monday. I've heard one or two people say it was only a wrist injury but it was a serious wrist injury that needed a major operation. It was bad. It could have been for the rest of his life so we had to make sure he got his wrist sorted properly.
"He has been able to do lots of running and lots of training but not anything with a football. Hopefully, next week, we will get 'Felli' back. We're beginning to get a few people back."