Fellaini has scored just one goal this season, in the Capital One Cup for Everton against Stevenage, prior to completing his transfer deadline day move to Old Trafford in a campaign disrupted by injury.
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And the Scot believes Fellaini is on the verge of making a breakthrough ahead of the Manchester derby on Tuesday night.
"They [City] have goalscoring midfield players and it’s important to have goalscorers all over the field," Moyes told reporters. “That contributes a lot to your goals.
"But we’ve got good midfielders. We still think Marouane Fellaini can get goals and he was unlucky on Saturday against West Ham.
"He should have scored with a header and then you could argue it was a penalty with the one where he went through [on goal], so I think he’s beginning to show signs he can get some goals for us as well.
"But I do agree they’ve got very good midfielders who are goalscorers."