Two of Zidane's sons, who play in the Madrid academy, were among 39 players investigated by FIFA with the club eventually sanctioned for breaking the rules regarding the signing of foreign nationals under 18 in eight cases.
"It seems absurd because they (his sons) have lived their whole lives here in Madrid with family and it will be fixed," said Zidane.
"The most important thing is that we know what has happened now. I think it will be fixed with time and next week we won't speak of this anymore."
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Madrid have signalled their intent to take an appeal all the way to the Court of Arbitration for Sport (CAS).
Atletico Madrid were hit with the same ban on Thursday and have also signalled their intention to appeal. However, Barcelona's appeal to CAS for a similar sanction in 2015 was rejected.
Under international football rules, players under 18 cannot be transferred to another country, except in limited circumstances and all transfers need the approval of a special FIFA committee.
Madrid must lodge an appeal with FIFA's appeals committee and if they are unsuccessful can then take their case to CAS.
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"It doesn't make sense. We will wait and see what happens next week. I am calm, it is an error and nothing more.
"The club will appeal. There are not just my sons, there are many players and families and I think it is an error."
Zidane is set to take charge of just his second game as Madrid boss at home to Sporting Gijon on Sunday.
But his preparations were further disturbed in an unsettling week for the club off the field as Madrid released a statement on Friday to confirm that Frenchman David Bettoni is just part of Zidane's coaching team and not assistant coach as he doesn't have the required licence.
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"David Bettoni is an assistant of mine, he works with me, but there are various (assistants). We have a team and David is one of them, he doesn't act as an assistant coach.
"We have Chendo who has the title of assistant coach."
On the field, Zidane will be without captain Sergio Ramos for the visit of Sporting with Raphael Varane set to deputise in central defence.
Otherwise, Zidane is expected to name the same team that thrashed Deportivo la Coruna 5-0 on his debut last weekend thanks to a hat-trick from Gareth Bale and two goals from Karim Benzema.
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