Parkinson's men head into their last-eight clash with Reading knowing that victory would put them into the semi finals of the competition for the first time since 1911 - the year of City's only triumph so far in the F.A Cup.
With City having only ever previously made it to the last-four of the competition in the year of 1911, any victory on Saturday would see the Bantams into the semis for only the second time in their entire history.
Parkinson: "As much as we have tried to play this game down while we've been having league games, this is clearly a huge match for all our players, staff and supporters.
"The F.A Cup is obviously a level above the Capital One Cup given its prestige around the world.
"When we made it to Wembley for the League Cup Final back in 2013 we spoke about making history. If we could get there again on Saturday, it would be the first time the club have played in a semi final since 1911.
"These group of players want to be remembered - that is what being in football is all about."
After beating Chelsea and Sunderland in the previous rounds, some neutrals may see Parkinson's side as favourities to progress this Saturday afternoon.
As the lower ranked side in the tie, however, Parkinson is keen to pick out that City still remain very much the underdogs going into the mouth-watering match.
Parkinson added: "We are just enjoying testing ourselves against higher level opposition.
"Right from the start of the season against Leeds United in the Capital One Cup, the Millwall game, the Chelsea game, the Sunderland game in the F.A Cup - the lads have relished the chance to test themselves against higher division opposition.
"All we can hope for is that the lads play to their very best against Reading.
"We are under no illusions, however, that we are going to have to play better than we have done at any point this season to progress.
"We don't fear Reading but we respect them.
"We will take the experiences from a couple of seasons ago in the Capital One Cup and from this season in the F.A Cup into this game."