The former France international has praised his former team-mate's start to life at the Bernabeu and has named his "ideal" coach
World Cup-winning midfielder Zidane took over from Rafael Benitez in January, having previously coached their Castilla side, with the club third in La Liga and two points adrift of arch-rivals Barcelona, having played a game more.
Zidane has made a largely positive start, although Sunday's 1-1 draw at Malaga leaves his side a point off second-place Atletico Madrid and now nine below champions Barca.
With La Liga success looking highly unlikely this term, Anelka warned his former international colleague that he will always be under pressure in the capital.
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"He likes football and he has the right qualities. He started with nice wins at the Bernabeu and I'm happy for him," the former Madrid striker told France Football.
"But it is only the beginning and the road is long. At Real Madrid, the pressure is very strong. You're never completely calm."
Benitez took over from Carlo Ancelotti in June last year after the Italian delivered the long-awaited 10th Champions League title during his time in the Spanish capital.
Anelka worked with the former Paris Saint-Germain and AC Milan boss at Chelsea and added: "Ancelotti is the ideal coach.
"Among those I have known, and there are many, he is certainly the one that stands out for me.
"He was a great player and he understands you. He brings out the best in everyone he leads. He's human, intelligent and he does everything so you can feel comfortable to express yourself.
"Once you're on the field you feel only one thing: I will give everything."