Parkinson's men will entertain the Championship side in a mouth-watering Capital One Cup Round 2 West Yorkshire derby in front of the Sky Sports cameras and an expected bumper crowd at Valley Parade.
Some bookies have made the Bantams slight favourites for the tie given Leeds' relatively slow start to their league campaign but Parkinson knows that his side are still very much the underdogs for the game.
Parkinson said: "I think it is important that we all understand how much this match means to our supporters and the people of Bradford - we will certainly be making the lads aware of it.
"We know we haven't beaten Leeds for a long time. Wednesday night is a great opportunity for us to make history.
"To do that, however, we have to raise our game to a level we haven't reached so far this season.
"We are going to be playing against a Championship side who have brought in a lot of players over the summer and spent a bit of money in doing so.
"Leeds have had an indifferent start to the season but the minute we think we might be favourites, or we are better than them, or that we don't have to play with the intensity and desire required then we won't get through.
"We will need that underdog mentality come Wednesday night.
"We are looking forward to testing ourselves against a Championship side because all of our lads want to play at the next level.
"We have an ambitious group of players who want to progress with Bradford and as individuals.
"This game is an opportunity for us to show the country that Bradford City as a team and as a set of individuals are good enough to compete at the next level up.
"To win a cup tie against a team from a higher division you have to raise your game - that is what we will be looking to do this Wednesday."