The Dutchman played over 100 times for the Bavarian club during a five-year period between 2006 and 2011.
He had a successful playing career, winning the Champions League with Barcelona in 2006 and reaching the World Cup final with Holland in 2010.
After spending his last year with PSV Eindhoven, Van Bommel retired in the summer, and now he could be set to return to football.
Rummenigge told Sky Deutschland: "We are in close contact with Mark. He has said he would want to return to become a coach in football.
"We had a good chat with him about the issue. He could imagine returning to Bayern as a youth coach."