Preston are chasing promotion from League One this season – consecutive victories recently putting them back into contention after a five-game winless run in the third tier.
The Lancashire club's home form has always been strong, however, having lost just one league game in the past 13 months and Grayson – who masterminded then-League One Leeds United's victory at Old Trafford in the 2009-10 FA Cup third round – sees no reason why his current crop cannot emulate shocks of the past.
"This tie does a lot for the football club," he said.
"It lifts the profile, it will be a fantastic atmosphere, brings in vital revenue and we have to go out and enjoy it and see where it takes us.
"We have nothing to lose and Manchester United certainly has.
"The one thing you don't want the team to do is to let it pass them by, because these games don't come around too often.
"You have to grasp it and somewhere down the line there might be a hero – and from becoming a local hero, they suddenly become a national and worldwide hero if they produce a performance and get a goal to knock Manchester United out of the FA Cup."
Grayson's Old Trafford goalscorer Jermaine Beckford is in his current squad and Preston have been boosted in recent weeks by the return to fitness and form of top scorer Joe Garner after three months out with a knee injury, while former United trainee Sylvan Ebanks-Blake and Premier League veteran Kevin Davies complete an intriguing set of attacking options.
Louis van Gaal has a nearly full squad to choose from, only Michael Carrick (calf) is definitely out, though Phil Jones may miss out with a knee issue and Robin van Persie is unlikely to be risked with an unspecified injury.
Wednesday's 3-1 victory over Burnley took a United side that have lost just one of their last 18 games up to third in the Premier League, but Van Gaal will take nothing for granted after being taken to a replay by Cambridge United in round four.
He told MUTV: "It's always the same because you know the world is for the underdog and we have to play away under the same circumstances as at Cambridge or Yeovil [Town in the third round], so it shall be very difficult.
"You know that they play more or less with two rows of four and a striker who is dropping in, as did Cambridge and Yeovil and also the last [league] games, for example Queens Park Rangers and Burnley. It is always difficult to play against a defending team.
"It's our goal to win a [trophy] and I hope to win one for the fans of Manchester United."
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