Kroos joined Real Madrid from Bayern Munich in 2014 and has gone on to help Los Blancos to two LaLiga titles and three Champions League triumphs.
Zidane has coached Kroos since 2016 over two separate spells, and the Madrid boss has no doubt that the Germany international will go down as a midfield great.
"He will be remembered as a spectacular player, one of the best in the world in his position," Zidane told Real France, as reported by TyC.
"When I arrived, well, you can imagine, I was really happy to be his coach.
"It's true, when I retire I will be able to say that I trained Cristiano [Ronaldo], [Gareth] Bale, [Luka] Modric, [Sergio] Ramos. But I will also say I coached Toni Kroos.
"It is impressive to see him train every day. How professional [he is]. Talking about him is talking about someone extraordinary."
Kroos' main skill, according to Zidane, is his patience and composure, and a player who leads by example.
"He is so good that he could play as a 'six' or even as a '10'," Zidane added. "You put him in and he adapts. His main virtue is his serenity, he's calm.
"He's not nervous and loves reaching out to shoot from afar as much as taking a back pass. The ease with which he plays with both feet is fascinating to me. You could come to think that he's a natural left-footed player.
"Toni is a very quiet and reserved boy. But when he speaks, he speaks to anyone: coach, managers, teammates. He does not stop. I have seen many discussions in which his participation has ended up being key."