The Toffees boss believes the former Standard Liege man could operate behind either one or two strikers, but is looking for him to add more goals to his game next season
The Belgium has predominately been positioned with a defensive mindset since his big-money move in 2008, although his manager is of the belief that his long-term position is further up the field.
Tim Cahill has long featured in the role, but Moyes has suggested that Fellaini could become the 32-year-old’s successor.
"Marouane is probably seen as more of a defensive midfield player," Moyes told the club’s official website.
"But he's far better when he's joining in and getting forward because he can do a bit of everything.
"He plays for Belgium as one of a three-man midfield. For us, we've tended to play with two midfield players and one ahead - in the main, that has been Tim.
"But I've always known that Marouane can do that job. We had just been looking at the right time to do that."
"He's far better when he's joining in and getting forward because he can do a bit of everything" - David Moyes
The 24-year-old has been a mainstay of the Everton side in recent seasons and Moyes is hoping his midfielder can replicate the performance he produced during the 4-4 draw against Manchester United at the back-end of last season where he ventured forward to join the attack.
"Marouane's performance against Manchester United was excellent, but I thought he has been in near enough all games," he added.
"He's been needing to add a goal or two to his game because when he first came he got 10, I think.
"He just needs to add a little bit more and his goal against United, his all-round play, even his setting up for the fourth goal for Steven [Pienaar] would have given him a lot of confidence.
"It's difficult to put him into any one box. He's got a goal in him, he does get forward and causes problems, but he's also very good at breaking the game up and doing other things. He's quite good at both jobs."
Despite joining for £15 million four years ago, Everton’s record signing, Moyes believes the club’s supporters are only now seeing the best the former Standard Liege man has to offer.
"You can see Marouane's enjoyed his football much more in the last three or four months,” added the Everton boss.
"Young players mature. The decisions you make as a young player are sometimes different than when you get a bit older.
"His form has been good. He's been getting us a couple of goals in recent games, and long may that continue."