The Belgian midfielder has been linked with a move to Manchester United in recent days after Toffees boss David Moyes was confirmed as Sir Alex Ferguson’s successor at Old Trafford.
But the 25-year-old says he is happy on Merseyside but admitted his desire to test himself against Europe’s finest.
“Every player wants to play in the Champions League. That is the big competition,” Fellaini said.
“I hope I can do it with Everton. I’m happy here. I’ve been at the club for five years. I’m happy because I know everybody.
“For my future, I want to play in England. The Premier League is the best league. Here there are five, six, seven, eight teams, all of whom think they are good enough to play in the Champions League and want that.
“There isn’t another country in Europe where you get that.”
MORE: The latest football news