He was sentenced to four years for his role as an accessory to the murder of 300,000 people at the Auschwitz concentration camp.
German magazine Der Spiegel said Groening died on Friday but prison authorities had yet to receive a death certificate.
German prosecutors say they have been notified that a former guard dubbed the "accountant of Auschwitz" has died.
At the age of 21, Groening volunteered to join the elite Waffen-SS before transferring in 1942 to work at Auschwitz, where he counted the money found among the belongings of prisoners and sent it to SS headquarters in Berlin.
He was also on several occasions assigned to "ramp duty", processing deportees as they arrived by rail in cattle cars at the Nazi German death camp in occupied Poland.
More than one million European Jews died between 1940 and 1945 at Auschwitz, before it was liberated by Soviet forces.
A court doctor had decided that Groening was able to serve his sentence, providing he was given appropriate nursing and medical care.
During the trial, Groening asked for forgiveness while acknowledging that only the courts could decide when it came to criminal guilt.
His case followed the conviction of former concentration camp guard John Demjanjuk, who was sentenced because he had served at the Sobibor camp in occupied Poland - rather than for crimes he was known to have committed.
After the war, Groening, led a normal, middle-class life in Lueneburg Heath in Lower Saxony, working at a glass-making factory until retirement.
He acknowledged "moral guilt" and said he was "very sorry" for his actions.
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