No other country is willing to accept the 87-year-old, the Cleveland Plain Dealer reported.
Demjanjuk's family and supporters are glad he can remain in Seven Hills, Ohio.
"We want him to stay here because we believe that's where he belongs," said Edward Nishnic, a spokesman for the family, calling the legal case "a very long, sad show."
Others see it as a miscarriage of justice.
"If John Demjanjuk is allowed to die in the United States without suffering the ultimate legal remedy under the law, it would be a tragedy," said Jonathan Drimmer, a lawyer who worked on the case as a federal prosecutor.
Demjanjuk was sentenced to death in Israel for being a notorious guard at the Treblinka death camp known as Ivan the Terrible. But he eventually won an appeal and returned to the United States.
A federal judge ordered him deported in 2005. The U.S. Supreme Court is expected to make a final decision next year.