Real president Florentino Perez defended the £42.5million transfer last week by claiming the German asked to leave because "he couldn't handle the pressure at Madrid."
But fellow midfielder Cazorla insists nothing could be further from the truth, however.
"No, I don't think that," he told Sphera Sports.
"He was at Real Madrid for three years and he showed his quality there.
"I don't know why he has left Madrid, but I am sure that pressure wasn't the reason.
"Mesut has played in big games and he has always turned up.
"I think he left for other, more personal reasons, and not because of the pressure he was under."