Real have long been credited with interest in De Gea, 26.
He almost swapped Old Trafford for the Bernabeu in 2015 before a deal broke down at the last minute.
And the Manchester United star is still being heavily linked with a move to the Spanish capital.
However, according to Diario Gol, Zidane has ended his pursuit of De Gea, apparently choosing to continue with Keylor Navas in between the sticks.
But they claim the decision say has a "hidden side" with the Real boss said to have his goalkeeper son's interests very much in mind.
Luca Zidane, 19, is already on the books at the Bernabeu.
And his dad was apparently concerned he wouldn't be able to rise through the ranks if De Gea joined.
Diario Gol say the France legend plans to promote Luca to the first-team in the medium to long term.
He made 15 appearances at youth level this season, conceding 23 goals and keeping two clean-sheets in the process.
The news is likely to come as a boost to United.
Starsport understand the Red Devils have told Real to forget about landing De Gea because he is not for sale.
Jose Mourinho also pledged to do all he can to keep the Spain star at Old Trafford last month.
He said: "[When will] David [play]?
"I think the first match against LA Galaxy in pre-season.
"I hope to play Joel Pereira against Palace and Sergio in the Europa final.
"David is top of the world and obviously we want to keep him."
