After finishing last term in seventh place, just outside the Europa League spots, the Belgian now wants to go one better and claim silverware.
The 24-year-old spoke to the club’s official website, revealing his ambitions for the forthcoming season: “First we have to start the season well; second, my aim is to win something like the FA Cup or the League Cup and to finish in the Europa League.
"I have been here for four years, so of course I want to win a trophy."
Fellaini was speaking at the launch of the Java Cup in Jakarta, were they will come up against Turkish giants Galatasaray as well as both Indonesia and Malaysia national teams.
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He said of the challenge they will face from the Turkish champions: “Galatasaray have very good players, and you are playing against a national team so they will be good players as well.
“I think it is a good test for Everton before the start of the season.”
The midfielder believes that the tournament will be ample preparation for the Toffees, before Manchester United visit Goodison Park on the opening day of the season.
He said: “That is why we need very good preparation because it will be difficult against Manchester United.”
Fellaini, who arrived in 2008 from Standard Liege is looking for his side to start well for the first time during his stint at the Merseyside club, adding: “I have been at Everton for four years and each time we have started badly so I hope this year we start well.”
And on his own health coming into the new season, Felliani claimed: “My body has had a month's rest so I will go to Finch Farm next week and I am happy to start back.”