Fellaini, a stand-out performer for the Merseyside outfit this season, has been linked with a move away from Goodison Park, with reports suggesting there is a £22million buyout clause in the 25-year-old Belgium international's contract which several major clubs could be looking to trigger.
But when questioned about that on Friday, Moyes said: "The plan is to keep all of our players.
"I wouldn't be talking about anyone's contracts if I can help it, and I won't do it now."
Regarding potential incoming personnel, Moyes added: "We are trying - we will look around and see what we will get."
One midfielder who is certainly remaining with Everton for the time being is Thomas Hitzlsperger, with Moyes confirming the 30-year-old would be extending his stay at the club until the end of the season.
Hitzlsperger, having been a free agent since leaving Wolfsburg last summer, signed a short-term contract with the Toffees in October that saw him through to this month.
The former Aston Villa, West Ham and Germany player has made seven appearances for Everton so far and asked about Hitzlsperger's future, Moyes said: "We have decided to keep him on. Thomas is going to stay until the end of the season.
"He has played a few games for us now, and he has been around the block a few times. He knows exactly what is required."