The Belgian was on the verge of joining Napoli during the summer transfer window, but the move was scuppered when he sustained an ankle injury.
However, Fellaini is determined to see off competition from manager Louis van Gaal's summer signings and earn a place in the Dutchman's starting XI.
"I want to fight for my place. The coach wants to play with the eleven players who make the best team. I want to be part of that," the Daily Star quotes him as saying.
"I've had a meeting with the coach before the start of the season where he told me that there is a lot of competition in the midfield. I told him that I wanted to compete for a place in the starting XI."
Fellaini joined United from Everton last year in a deal worth £27m.