The Belgian midfielder has been the subject of intense transfer speculation in recent months, with suggestions the 25-year-old will leave Goodison Park at the end of the season, should the Toffees fail to qualify for the Champions League.
Chelsea owner Roman Abramovich has been credited with a long-term interest in bringing Fellaini to Stamford Bridge; a move that would see him link up with international team-mate Eden Hazard in west London.
However, the Blues could now face competition from newly crowned Premier League champions Manchester United, as Old Trafford boss Sir Alex Ferguson plots a rival bid for the midfielder's services.
Fellaini has been in impressive form for Everton again this season, which is the reason why he has attracted admiring glances from a number of clubs. However, Moyes - whose own future on Merseyside is by no means certain, with his contract set to expire at the end of 2012/13 - sees the player as a big part of the club's future plans.
"He is a big part of our squad not only because of his size but also because of how important he is to us," the Scot told Yahoo Sport.
"He is someone that we will be more than happy to see here again next year at Goodison."