The former centre-back decided to join Werder Bremen instead of Bayern when he left Hannover in 2006, before eventually moving to the Gunners.
Mertesacker told Bild: "When I played for Hannover I had several offers, also - as I have been told - from Hamburg, Bremen and Bayern.
"Back then I already was a German international and Bayern would have loved to have the complete German national team.
"But Bremen with [Tim] Borowski, [Torsten] Frings, [Miroslav] Klose and [Frank] Baumann also had some German internationals, which was more attractive for me.
"I still lived at home with my parents at 20/21 so the family was still close and I preferred that. And back then Bremen had the reputation for helping young players make their next step!
"But maybe I didn't make the move because my granny said: 'Bayern doesn't work at all'.
"She didn't like Bayern and died before I made a move. I guess she would have turned in her grave and said: 'Not with me!'"