The 61-year-old has come under pressure to quit after reports that he was arrested on March 20, then released on bail for €5 million euros as part of an investigation into unpaid taxes.
According to magazine Der Spiegel, Hoeneß will make his announcement at Monday's executive board meeting.
The report claims, the Bayern board, which contains several major figures in German industry, had wanted Hoeneß to resign permanently as president before the Champions League final against rivals Borussia Dortmund at Wembley on May 25th.
But after last Wednesday's 3-0 victory in Barcelona gave Bayern a 7-0 semi-final win on aggregate, the fans' euphoria forced the board into a change of heart and Hoeneß will be allowed to stay in office until the final.
In an interview last week with German newspaper Die Zeit, Hoeneß had ruled out resigning before the European final, but admitted he was "in hell" due to the tax evasion allegations.
Reports first broke on April 20 that Hoeneß had substantial sums of cash in a Swiss account and had failed to pay millions of euros in tax on the interest.
The revelations sparked huge controversy in election-year Germany, which is looking to crack down on tax evasion, and even German Chancellor Angela Merkel admitted she was "disappointed" in Hoeneß' conduct.