In December the 18-year-old claimed he had met with Zidane in 2013 to discuss the possibility of joining Madrid's youth ranks, only to instead commit to the Stade Louis II.
He made his first-team debut in 2015 and has begun to make a name for himself this term, becoming the youngest player in the last 30 years to reach 10 Ligue 1 goals, beating the likes of Thierry Henry, Eden Hazard and Karim Benzema to that milestone.
Speaking ahead of his team's trip to face Athletic Bilbao in La Liga on Saturday, Zidane acknowledged discussions had taken place, but stopped short of confirming Madrid are still interested in bringing the exciting forward to the Santiago Bernabeu.
"He almost signed for Real Madrid but then he went to Monaco," he said.
"I can't speak about this. We know he's a good player, what he's doing at his age is fantastic, but that's it. What I'm interested in is what we are going to do tomorrow. But he was about to sign here, yes."
While Mbappe has earned a first call up to the senior France side, compatriot Raphael Varane was not selected by head coach Didier Deschamps for the matches against Luxembourg and Spain, as the Madrid defender continues his recovery from a hamstring injury.
"I don't think he was ready to travel and play with the French national team because he's just getting back from injury and he's not 100 per cent yet," Zidane said. "I think it was for the best that he's going to stay here with us."
The match against Spain, which will take place in Paris on March 28, prompted Zidane to recall a friendly between the countries at the same venue, settled by his goal, in January 1998, the year in which Les Bleus went on to win the World Cup.
"It's a magnificent friendly," he said.
"I remember that famous game in 1998… and to be able to play and score in the Stade de France was special. France are getting back to their best. It's going to be a great game. We know that Spain have been European and world champions but so have France."