The row happened after Labour failed to sign up fully to the internationally-recognised International Holocaust Remembrance Alliance (IHRA) code of conduct.
Dame Margaret, a secular Jew who lost relatives in the Auschwitz death camp, published a three-page letter to her lawyer dated July 25 from Labour’s general secretary Jennie Formby.
It says a “warning and reprimand” from the party’s chief whip would allow an end to the investigation, “on condition your client gives in short order an appropriate apology for her conduct”.
The letter says there is “no threat” against Dame Margaret but suggests the possibility of suspension.
Dame Margaret said: “I’m still no wiser as to what I’m accused of, the nature of complaints received, who the investigating officer is or what the timeframe for the investigation will be. Is this fair?”
Reports suggest Mr Corbyn could be gearing up for a climbdown speech over anti-Semitism in Labour next week.