However, the Australia international severely bruised a foot in Wednesday's 1-1 draw with Arsenal and is a major doubt for the trip to Old Trafford.
If that was not bad enough Fellaini, who returned against Arsenal after a two-match suspension, is also troubled by an injured shin.
"Both players are struggling and I won't take any chances if I don't think they are not going to be fit," said Moyes, whose side are unbeaten in their last seven Premier League matches.
In the last fortnight Everton have drawn against Liverpool twice (once in the FA Cup) and Arsenal but must now try to get something from United – who have just set a record for 11 successive clean sheets.
Moyes is delighted with the way his side, who are sixth in the table, have coped without a recognised striker but knows that effort cannot drop at Old Trafford.
"It has been a tough period but I have to give credit to the players for the way they have gone about it," said Moyes.
"We are working with a small number who have put themselves on the line and over the line most weeks so I have to say well done to them.
"We have had to dig really deep to earn a point in some games, in some of them we could have taken a chance more than we did.
"You just have to keep persevering. There's no secret to it – if there was I'd have done it.
"This is the biggest test because you are playing the world champions, European champions and Premier League champions.
"But we are playing like champions, in our own minds. When you think that way you can go to Old Trafford with confidence."
Moyes added: "It is a big ask. Lots of teams have played them recently and not been able to score so we understand how difficult that is going to be.
"But in the same breath we have been hard to score past as well. We will need go to Old Trafford and make sure they don't score easily because you don't tend to score many past them.
"Hopefully if we get our moments we can try to take our chances."