But his lawyers are to mount another legal appeal, arguing that he is unfit to spend time behind bars, the Daily Mail reports.
Groening was known as the "Accountant of Auschwitz" because he was responsible for sorting through the possessions of the doomed and sending cash and valuables back to his SS masters in Berlin.
He was sentenced to four years in prison in July 2015 by the State Court in Lüneburg for aiding the murder in at least 300,000 cases.
His testimony about the wholesale slaughter of innocents in the camp, where an estimated 1.2 million people were murdered, was considered historically important in refuting the claims of Holocaust deniers who persist in the lie that the murder of six million Jews never happened.