Sir Alex Ferguson’s side have won the competition more times than any other side, last winning the cup in 2004, but are yet to lift the trophy at the new Wembley.
Giggs first won the FA Cup in 1994, and despite winning the competition a further three times as a player, the 39-year-old confessed how much the famous cup means to him, revealing that he is hopeful of winning it once more before he hangs up his boots.
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"Winning the FA Cup was one of my first memories as a United player," Giggs told reporters.
"The competition was huge for me growing up and still is and we have so many players here who are desperate to win it."
Giggs is keen to avoid an FA Cup replay against Fulham, after admitting that Manchester United are well aware of the challenge they face against the Cottagers.
He has full faith in the Reds Devils’ strength in depth, but with their Champions League clash Real Madrid looming in the horizon, Giggs insists how vital it is that the club progress to the next round at the first time of asking.
The former Wales international said: “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.
"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."