Wenger is set to depart Arsenal after 22 years at the club. He will leave the position at the end of the summer, but his future in football is unclear.
Some believe he may retire, while others feel a top job like Paris Saint-Germain could tempt him back into the game.
Speaking at a press conference at the club on Friday, Gazidis said: "He is somebody who is in great shape.
"He still has that competitive edge as he always has but that is really a question for him."