Fellaini, 23, has become a key player for Everton since signing for a club-record fee from Standard Liege in 2008, and his father has claimed Chelsea are considering a bid.
"The big clubs can see what a good job Marouane is doing and that is why Chelsea are following him intensively," Abdellatif Fellaini said. "In his position he'd get into the starting XI at any big club."
Fellaini, a Belgium international, remains under contract at Goodison Park until 2013 but, having been forced to cash in on Steven Pienaar in January, Moyes is eager to speak to the player about an extension to his current deal.
"I think talks with Fellaini will start shortly because we don't want to encourage clubs," Moyes said. "We don't want the speculation to start, so hopefully we will get him sorted.
"People will look at our club and think that we're a selling club - that we might be vulnerable. In the main, we have never had to sell our best players. The ones that have left have left because they wanted to.
"I've always had the final decision and I hope that stays the case."