The Los Blancos legend assisted Ancelotti when Real won the Champions League and Copa del Rey in 2013/14, but was in charge of their Castilla side last term.
Madrid sacked Ancelotti in May and replaced the Italian with ex-Napoli and Valencia boss Rafa Benitez.
"Yes, I would have accepted the task of being Ancelotti's successor," Zidane told France Football on his 43rd birthday. "I am a professional and never refuse a challenge.
"But no, I am not disappointed I was overlooked in favour of Benitez. It was felt by the board that now was not the time for me to take over. These things happen naturally, one should not force them.
"It was not meant to be on this occasion. Madrid president Florentino Perez chose another coach, and that's that."