Following Saturday's goalless draw at Gigg Lane, Parkinson's Bantams and Bury were selected at home to Hull in Monday night's televised fourth round draw.
City and the Shakers will meet again at the Coral Windows Stadium next Tuesday (19 January 2016) for the right to host Hull - the 2014 FA Cup runners up - at the end of the month.
Parkinson said: "We are pleased with the home draw. It is a tie against a big side from this region if we can get past Bury in the replay.
"If we can go through (in the replay), I think it will be a terrific atmosphere for the Hull tie.
"Steve (Bruce, Hull City boss) has a tremendous squad there and this match might be an opportunity for him to give some of his other players a chase to shake a claim.
"I would imagine Hull's priority this season would be try and get back into the Premiership but it will still be a tough challenge whoever Steve goes with for the game against ourselves or Bury.
"We haven't had too many home matches recently but we now have a whole batch of them coming up regardless of what happens in the cup.
"We are looking forward to that, we can't wait to get back on home soil and in front of our own fans at the Coral Windows Stadium.
"We have worked hard to get this far in this competition and we still have plenty to play for.
"Saturday's tie at Bury was a tough game for everyone, we all had to roll our sleeves up for that one.
"With the incentive of a home tie waiting for the winner's in the next round, we now have to get back to Valley Parade and try to finish the job off next Tuesday."