Zidane's eldest son Enzo Fernandez left Los Blancos for the Basque club in June and could be in the XI for the hosts at Mendizorrotza this weekend.
Asked how he felt about going up against the 22-year-old midfielder, Zidane told a news conference: "I hope he doesn't score! We are both very competitive, him for himself and me for me.
"It will be a little bit strange but I'm happy for him, he's working hard, he's at a side that is not doing great at the moment but they've got a good squad and they are working well.
"But tomorrow we are up against each other and I'm on the Madrid side, he's on the side of Alaves. It is going to be competitive - that's all."
Questioned further about what the match will mean to him on a personal level, Zidane said: "[I'm] not really thinking too much about that.
"Yes, of course, in some ways it will be a bit more emotional but it's Real Madrid against Alaves, nothing else.
"That's the most important thing for me. He's very competitive and I am as well. We will both do everything possible to try to win, although I'm not going to play and he is.
"I've always watched him as a player. I speak to him as a father. He was with me last year.
"At the moment I'm not his coach, I'm his father. I don't have to give him any tips about football at the moment. The relationship is father and son.
"When we talk that is all we have in the relationship."
Both teams are in need of all three points, Madrid having won just once in their last four La Liga games, including a 1-0 defeat at home to Real Betis last time out.
Alaves are second bottom and are yet to avoid defeat in five league fixtures this season.