Following City's tremendous win over Premier League side Sunderland on Sunday, Parkinson's men were pitted against the Championship side in the last eight of the competition.
During his playing days, Parkinson made 425 appearances for the Royals during an 11-year career with the Berkshire-based club. As a result, Parkinson remains a hugely popular figure at Reading to this day.
Parkinson said: "We wanted another home draw and any draw at home at this stage is a good one for us.
"I don't think anyone can complain about this draw - it is a good opportunity for us and I'm sure it will be a great occasion.
"The priority was to get a home tie and it will now be another good chance for the people of Bradford to come out in their numbers.
"It will be great for myself and my family to be playing against Reading. I spent some great years at the club and I have some good friends still at the club.
"My kids were also born there.
"Reading are a good club with strong foundations, that is why they have had success in recent years and spells in the Premier League.
"Once our dressing door closes, however, and we're ready for the game, we will be focused purely on our performance and trying to win the game.
"Both the team and the supporters quite rightly received plaudits after Sunday's game. We now need more of the same.
"We need to get every seat we can sold for the match and get the place bouncing again, that is going to give us an advantage.
"We want to get as many Bradford fans into the ground as possible."