The League One side travel to Stamford Bridge looking to cause a major upset against the seven-time cup winners.
City have come through three ties to reach this stage of the competition, as they take their place in the fourth round for the first time since 2000, when they were a top-flight club.
And Parkinson has urged his players to relish the opportunity presented to them on Saturday.
"The lads have fully earned the right to get this far in the competition and to make the most of a game like this,” he told the club's official website.
"We will enjoy the preparations and the extra attention that comes with it.
"We've come through a tough local fixture at Halifax, beaten Dartford and then overcome a side from the league above us [Millwall].
"We now have this fantastic tie to saviour against a top team and a top manager. We will be giving it everything we have this week to make sure we play to the very best we can come Saturday."
Bradford are likely to face a changed Chelsea side from the one that drew 1-1 with Liverpool in the first leg of the League Cup semi-final on Tuesday.
Chelsea boss Jose Mourinho has the luxury of a fully fit squad from which to choose as he goes in search of a ninth win in 12 games in all competitions, a run which includes the 3-0 home victory over Watford in the previous round.
The likes of Didier Drogba, Andre Schurrle, Ramires, Loic Remy and Mohamed Salah are all in line for a potential start.
Bradford will check on the fitness of striker Billy Clarke, who stepped up his recovery from a knee injury when he travelled with the squad to the Bristol Academy of Sport in Filton ahead of last Saturday's 1-0 league defeat at Yeovil Town - a result that left City sixth in League One.
They will also monitor defender Andrew Davies, who suffered a slight tweak in the latter stages of the game at Huish Park.
Parkinson and his assistant Steve Parkin will be able to sit on the bench at Stamford Bridge, despite being sent to the stands following a melee involving both sets of players during the third-round replay between City and Millwall, which the former won 4-0.
The pair have both since been charged with improper conduct by the Football Association, who have also charged both clubs with failing to ensure their players conducted themselves in an orderly fashion.
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
‘He’ll still be playing at 40 at a good level because he’s in such good shape and looks after himself so well. He does everything to be a top professional’: Ex-Liverpool coach insists Mohamed Salah has plenty more miles in the tank
