The Yorkshire side travel to the Emirates Stadium hoping for a similar performance as last year after they were minutes away from causing a shock, with the Barclays Premier League side needing an injury-time equaliser from Cesc Fabregas to earn a replay, which they went on to win 3-1 at Elland Road.
And Grayson is hoping his side remember the qualities that served them so well last term.
"It is an opportunity for the players to go and play against some of the best players in the country, if not Europe and it gives the profile of the club a big lift again," he said.
"I think Arsenal are a different team and we are a different team but you have to learn from the experience of going there and how well we coped with the situation.
"We know what we need to do. We are going there as underdogs but we will go there to enjoy the occasion and the game but do ourselves justice as well.
"Last year we got so close, to concede a penalty late in the game after we played ever so well hurt. We have got to go with the same sort of confidence and ability and anything could happen.
"It is a no lose situation in terms of the game. We won't be going gung ho because Arsenal on their day can destroy any team.
"We will have a game plan and stick to it, pass the ball and hopefully create chances.
"There is always one shock in the FA Cup third round, why can't it be Leeds beating Arsenal?"
Grayson's side look certain to come up against Thierry Henry after Arsenal's all-time leading scorer rejoined on a loan deal from the New York Red Bulls.
The 34-year-old Frenchman took a liking to playing against Leeds during his first stint in English football, scoring 11 goals in his five seasons of lining up against them, and Grayson has labelled him as one the the "best Premier League players ever".
"The pace and the goalscoring opportunities he used to create, he has to be one of the best, without a doubt," he added.
"He could make anything happen and that is a fantastic attribute that Arsene Wenger has for spotting players.
"He has a different experience of playing in America but it is probably fitting that he comes back and has a couple of months with Arsenal.
"We don't expect him to be like he was but he will still be a considerable threat if he plays."