The two teams will meet in the first round of the competition at the Crown Ground on the week commencing August 10 after the draw was made on Tuesday.
Windass snr works for Hull as a club ambassador after starring for them over two spells and scoring the goal that sent them to the Premier League for the first time in 2008.
He will have mixed emotions though when he sees his son Josh – a midfielder with Accrington for the last two years – trying to knock them out at the first hurdle.
The 46-year-old said: “With me being an ambassador of the football club and then my son playing for Accrington, it has made it a bit tasty for me.
“I wish I was still playing so I could play against him. It will be a great occasion for Josh and he will obviously get a lot of publicity with it as well.
“He’s a good footballer, he’s got a great future and if you want to be a top footballer, you’ve got to play against good players.
“He’ll certainly be playing some good players against Hull City and we’ll see where it takes him. I obviously want Hull City to win as I’m a Hull lad.
“The perfect situation for me would be a final score of Hull City 4, Accrington 3, with Josh getting a hat-trick then we’ll all be happy but I don’t think that will happen.
“If Josh does score, I’ve got to be careful if I’m jumping up. If he scores and they’re winning 1-0, I’ll have to keep my bum on the seat I think.”
A treble from Windass Junior is unlikely given he has only scored six times in 51 appearances so far but he will go into the tie with optimism.
He added: “It’s a great draw for me personally and for the club. My dad rang me this morning to tell me I’m lucky he’s not playing. Hopefully we can cause an upset.
“He has given me a bit of stick but he’s happy with the draw. He obviously works for Hull City so he’ll be able to come to the game and it will be good for both of us.”