The pair played together for Ajax and Inter.
Van der Meyde told La Gazzetta dello Sport: "For me, Chivu will always be a boy, a year younger than me and already wearing the captain's armband at 21.
"Ajax is a different planet from all the others: there they don't look at your ID, but if you're so precocious, you certainly have something special. Cristian was a natural leader in the dressing room, respectful, always smiling: I'd call him a true gentleman. I'm not surprised he's a coach today: these early problems are part of the job.
"The defeat against Juve, in my opinion, was undeserved."
Asked if Chivu took the Inter job too soon, Van der Meyde continued: "Who decides? If you're into this profession, there's no time constraint. From Parma to Inter is a big leap, but the club's management is aware of it: they trust him and have placed their faith in him.
"It's still a gamble, but I think he can win it. I think there's still some residue from the recent past. The Champions League was a terrible disappointment, (Simone) Inzaghi left, and there was some controversy in the transfer market. Chivu needs to work on his mental health."