Richard Glossip faces execution after being convicted of murdering his boss, but he claims he has been framed.
The 52-year-old was sentenced to death on the basis of evidence from a colleague who said he ordered the murder.
This evidence meant the colleague was jailed and avoided the death penalty himself.
He has now lost a last-minute bid for a retrial to avoid his execution but a campaigning nun has intervened.
Sister Helen Prejean, a prominent campaigner against the death penalty, said if the execution goes ahead it is "very likely that Oklahoma will add the death of an innocent man to this record of mistakes".
Mr Glossip's lawyers claim they have a statement from a prisoner who claims to have overheard his colleague boast about implicating him.
There is now a chance for a last attempt to save him at the US Supreme Court.
Sister Prejean and Oscar winning actress Susan Sarandon have made several appearances on US TV appealing for clemency.
"With the U.S. Supreme Court's recent refusal to look at the constitutionality of the death penalty, it falls on the people of Oklahoma to take a deeper look, not only into Glossip's case, which is greatly flawed with loopholes, but at the faults of our system of capital punishment," the nun said.
She added: "The outcry of the people is fair, people have a sense of justice - and they say 'well he's had these trials,' but then they say, you mean a man is going to his death on the word of a 19 year old kid, who was under threat of the death penalty himself, who saw a lawyer one time.
"He delivered to them what they needed to save his own life.
"There's not a fingerprint of Richard Glossip's on the money, there's no forensic evidence to corroborate what Sneed said.
"Solely on Sneed's testimony Richard Glossip is going to his death."