WASHINGTON — A person familiar with the matter says the Justice Department plans to appoint a well-known New York attorney to run the fund that will be used to compensate Ground Zero workers who say they’re suffering illnesses due to their work amid the wreckage of the Sept. 11 terror attacks.

The person says the appointee is Sheila Birnbaum, who previously served as the mediator in lawsuits brought by families of the victims of Sept. 11. The person who confirmed her selection spoke on condition of anonymity because the decision has not been publicly announced.

The Wall Street Journal first reported Birnbaum’s appointment.