It was revealed earlier this year that the 61-year-old was the subject of suspicion but, although he has offered his resignation, the club has decided that he will remain in his current role.
"The supervisory board of Bayern Munich has had a meeting to look at the tax case concerning president Hoeness," a statement on the club's official website reads.
"Hoeness offered the board to resign from his office until the authorities in charge have decided over the possible clearance of a sentence due to his voluntary declaration. Hoeness has declared his regret over the incident and apologized.
"In the interest of Bayern Munich, who should be fully focused on achieving their goals in the Champions League finals on May 25 and in the DFB-Pokal on June 1, the board has decided that Hoeness should keep his post as president. The board will closely observe the matter and will pick up the topic again, should new insight come to our attention."