The 11-time winners of the trophy needed a replay against West Ham United in the last round to set up the home tie this weekend.
The 39-year-old told Sky Sports News: "You want to be challenging on all fronts given the strength in depth we've got. But we are quite keen to avoid a replay because we've got a lot of games coming up.
"Winning the FA Cup was one of my first memories as a United player. "The competition was huge for me growing up and still is and we have so many players here who are desperate to win it.
"We realise tomorrow will be a difficult game. Fulham did well when they came to Old Trafford earlier in the season and we're going to have to be at it right from the start."
Fulham face United at Old Trafford in the evening kickoff tomorrow.