With 11 final victories, United are the competition's most successful side, but it's nearly 10 years since they lifted the famous old trophy.
Cleverley, 23, said of the fourth-round clash with Fulham: "It means a lot. Our last FA Cup win was in 2004 and it's a trophy I want.
"Playing at Wembley is one of the best feelings of your career. I've been lucky enough to have played there five or six times but I always want more.
"We've got a few players who haven't won anything in this country yet - like me. So anything we're involved in, I want to win."