The Frenchman's team will play host to the Spanish champions, who also happen to be managed by his father Zinedine, this weekend.
Zidane said that it will be "weird" lining up against Real, but admitted it is an opportunity he is relishing.
"It is going to be weird, but also a very special match for me," Marca quotes him as saying.
"My father has always been an example to me, he was a great footballer and I always took notice of the things he was doing.
"I have arrived here from the comfort of being at Real Madrid and I am lucky to have arrived at a club that has been very welcoming to me."
Zidane spent most of his youth career at Los Blancos, rising through the ranks of their C and B teams before joining Alaves this summer in search of first-team football.