The Spain international, 24, left Madrid for Bayern on loan in January after making just five appearances for the LaLiga giants in the first half of the season.
Odriozola said Madrid head coach Zidane did not want him to join the Bundesliga side, where he has played just twice since arriving.
"I have contact with players and club employees and even with the doctors. Zidane is focused," the right-back told El Chiringuito de Jugones on Wednesday.
"When it came to talk about the departure I had several conversation with him and he showed me his support in private when Bayern were interested. Zidane did not want me to leave Madrid.
"It is appreciated that a figure like his thought more about me than himself. He is a great coach and a great person."
Odriozola joined Madrid from Real Sociedad for a reported €30million in July 2018.
A four-time Spain international, he is eager to succeed at Madrid, saying: "I dreamed of being a footballer.
"I have played for Real, I belong to Madrid and I am on loan at Bayern. Among my dreams is to succeed in Madrid. I really like to dream.
"I have fulfilled almost all my dreams and among those I have left is to succeed in Madrid."