The Gunners have won only two of their seven matches since the Spaniard took charge in December, replacing Unai Emery.
But Cazorla told Goal: "Yes, I believed he would become a manager in the future. Even when I was playing with him, he showed great leadership in dressing room.
"I believe he can become a great coach."
He added: "It's not easy for any manager now to be like [Arsene] Wenger or [Sir Alex] Ferguson. I can't anticipate how long he'll stay at Arsenal, but I believe he can also make great career at Arsenal, and he's a proper one for Arsenal.
"I hope Mikel leads Arsenal well."