Despite Leeds' relegation in 2004 and their subsequent drop into the third tier two years later, a bitter rivalry still exists between the clubs.
And Grayson - a lifelong Leeds fan - is confident his players can thrive on the occasion and possibly make a mockery of the 12/1 odds they have been priced at to win the game.
"We're in a decent run of form and we're very confident in what we can try and achieve," said Grayson, whose men have lost just once in the league this season and are unbeaten in 15 games.
"I feel we have got some talented players that can perform, certainly in the next level and hopefully the next level after that, but the proof will be in the pudding on Sunday. Hopefully we will be able to handle it.
"We're going into the game with a huge amount of confidence and belief. We're defending well and look like we're going to score at most times but this (Manchester United) is the best team in Europe.
"We want to go and enjoy and thrive on the experience and hopefully by the end of the game we'll have learned a great deal about ourselves. They will believe by the time the kick-off comes around that's for sure. The last thing I will tell them is good luck, and make sure you win the game."
Leeds last won at Old Trafford in February 1981, when a Brian Flynn goal earned them a 1-0 success, and Grayson has called for someone to step into Flynn's shoes and rewrite the history books.
"I saw Brian a few weeks ago and he told me it was him that scored," he said.
"Hopefully somebody else will be in the record books for scoring the winning goal against Manchester United."
Grayson, who is without the suspended Leigh Bromby and the ineligible Max Gradel and Sam Vokes for the contest, is not the only Leeds fan associated with the club's first team.
Captain Richard Naylor has been a supporter since his childhood and joked in the build-up that his friends have been texting him ever since the draw was made asking him to "smash Gary Neville".
But he too is confident Leeds can give a good account of themselves - preferably against the Red Devils' strongest line-up.
"If you're going to get a decent result you don't want anyone to have any excuses and if we're going to get a decent result we'd like to do it against a first-choice XI," he said.
"We're in decent form and we've got to take it with us."
Man. Utd v Leeds. Click here to bet.