Fellaini's future at Everton has been the subject of speculation with the likes of Chelsea and Manchester United credited with an interest in the midfield powerhouse.
Everton could face a fight to keep hold of the influential midfielder this summer after another impressive campaign on Merseyside.
However, Moyes sees Fellaini as a big part of his plans and wants to see him stay at Everton.
"He is a big part of our squad not only because of his size but also because of how important he is to us and he is someone that we will be more than happy to see here again next year at Goodison," Moyes told Yahoo Sport.
Meanwhile, Moyes admits Everton will find it hard to replace Phil Neville when he quits the club at the end of the season and he expects the Toffees captain to move into coaching at some point in his career.
"He has been really influential," added Moyes. "He has been a great captain and a great player since he joined us eight years ago and will be missed. He has been someone that I can rely on both on and off the pitch.
"I have got no doubt that he will go on to work in football and he is someone who we will miss. It will be a hard position to fill because the way he has captained the team has been excellent over the years.
"Phil will be a success in whatever he does in life because he conducts himself well and is very articulate but if I was a betting man I would say that his next step after playing would be coaching."