Midfielder Enzo, 22, left Real's reserve team in the close season in search of first-team football at Alaves, where he has made two La Liga appearances so far.
But with his side already seven points behind early league leaders Barcelona and in desperate need of points, Zinedine will put his job over family ties.
"I hope he (Enzo) doesn't score, we've got to look after our interests," said the 1998 World Cup winner.
"I haven't thought about it much. I'll have my own feelings but the match is Alaves against Real Madrid, that's the most important thing for me."
Zidane's 19-year-old son Luca could also make the trip as Real's third-choice goalkeeper, and like Enzo, he has played for the French Under-19 team, while his younger brothers Theo (15) and Elyaz (11) also play in Real youth sides.
Former Ballon d'Or winner Zidane said that he has not had a hands-on approach with Enzo's career since he left the Santiago Bernabeu, after giving him his Real debut in a Copa Del Rey match last year, in which he scored.
"I'm not his coach, I'm his dad and I don't have to give him anything in terms of football. When we speak, it's nothing more than a father-son relationship."
Although his dad might not be willing him on, Alaves could do with a goal from Enzo on Saturday, as they sit second-bottom in the early table, without a point or a single goal in five matches.
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