Kubo signed for Los Blancos earlier in the summer and has impressed in pre-season, but Zidane won't rush him into action once the campaign begins.
"There are many players who have come on pre-season with us from the youth system.
"Kubo has joined us recently and he is a player for the future, but we will talk about what is best with him and it could be good that he trains with us and plays for the Castilla, we will see.
"He is still very young and we must be patient with his development."
The Japanese playmaker, who turned 18 in June, has been one of few highlights from a disappointing pre-season for Real, who have suffered defeats to Bayern Munich, Atletico Madrid and Tottenham Hotspur.
AS' Robbie Dunne singled him out for praise during Los Blancos' 3-1 loss against Bayern in July:
He featured against Spurs and Fenerbahce in the Audi Cup, with Madrid losing 1-0 to the former on Tuesday and beating the latter 5-3 on Wednesday.
SB Nation's Kiyan Sobhani and ESPN FC's Dermot Corrigan were impressed with him:
Prior to joining Real this summer, Kubo made 16 appearances for FC Tokyo in 2019, contributing five goals and four assists along the way.
At the start of the summer, he was included in Japan's squad for the Copa America, with the Samurai Blue naming a young side in preparation for the Tokyo Olympics next year.
Although Japan did not make it out of the group stage, he helped them pick up draws against Uruguay and Ecuador, and stood out while doing so:
Last season, Vinicius Jr. broke into Real's first team at the age of 18 and had an impressive impact, so it is possible other youngsters could do the same.
What's more, with Marco Asensio set to miss the majority of the campaign with injury and Zidane having little faith in Gareth Bale, there's scope to earn a significant number of minutes on the right flank, which is where Kubo spent much of his time at FC Tokyo.
All young players develop differently, though, and performing for Real's senior side in competitive fixtures is a big step up from what he's done so far.
Dropping him in at the deep end could have an adverse effect on his development, so Zidane's caution could be a wise move at this stage.