The 23-year-old has less than two years left on his current contract with Everton and talks have been going on for several months regarding a new deal.
“I think it is very close to getting done,” Moyes told the club’s official website.
“The chairman and the chief exec have been working on it for a while and I’ve been waiting on the good news and hopefully it’s not too far away
“He has been a really good player for us over the last few seasons and if we can keep him it will be really good.”
Fellaini joined Everton in a £15million move from Standard Liege in 2008.
