The 25-year-old has enjoyed an impressive start to the season, with the Belgium international scoring eight goals in 16 appearances in all competitions.
However, the midfielder has been linked with a move away from Goodison Park in recent weeks, but Fellaini intends to see out the remainder of his current deal which expires in 2016.
“I want to go higher in football but I have a contract with Everton until 2016 and, if they want me to, I will see it out to the end,” said Fellaini.
Fellaini has scored 28 goals in 153 appearances for Everton after completing a £15m move from Standard Liege to the Toffees in September 2008.
He was handed a three-game ban after the FA punished the Everton midfielder for violent conduct during their 1-1 draw with Stoke City.
“The best person you have to look at is Lionel Messi. Every person targets him, they’ll do everything,” Moyes said.
“But all he ever does is get up and get on with it. That’s the sign of a top player. It says to people, ‘Whatever you do, it doesn’t affect me’.
“I tell Felli that you just have to get on with it. If I was playing against Felli, I’d try and wind him up.”