The midfielder left Everton last week for £26.5 million.
Fellaini said: "Everton was a great club for me with great teammates.
"I respect the fans but it is time for me to leave and join a big cub. I want to play midfield defensive and if I can help the team further forward then good. Training is quicker than at Everton but I'm happy.
"The quality is better than Everton but Everton are a great club as well. The price is not my problem. 25million or 30million or 20million - whether you are expensive or not, players are just players.
"In the past you have had Cantona. Roy Keane, Beckham - I will do my best."
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