Ozil is in talks with the Gunners over a new deal, with the current one running out in June 2018.
Ballack feels he should not extend his stay at the Emirates and should return to Germany.
“Mesut is an amazing player. He knows that he is one of the undisputed stars at Arsenal,” Ballack told Sport Bild.
“A lot of clubs would love to have him.
“But if he wants to win a major title, he has a bigger chance to achieve that at Bayern.”
Ballack also admitted that Arsenal will not allow Ozil leave except a big transfer fee is paid.
“If you look at the recent developments in England and China, it seems inevitable that Bayern will soon pay transfer fees of €50million or so as well,” he added.
“They have to if you want to keep competing with the best.
“If you want to bring in a world-class player, you will have to invest.”