The three inmates who famously broke out of Alcatraz prison in 1962 may not have gone down to their watery graves in shark-infested San Francisco Bay after all, according to a report.

According to a letter allegedly written by one of the three convicts in 2013, they all survived their daring escape.

“My name is John Anglin. I escape from Alcatraz in June 1962 with my brother Clarence and Frank Morris. I’m 83 years old and in bad shape. I have cancer. Yes we all made it that night but barely!” said the letter, obtained by local CBS affiliate KPIX.

He then tries to strike an astonishing deal with the FBI — offering to be locked up again for a year in exchange for medical care.

The feds have reopened the ancient cold case as a result of the shocking piece of evidence, which was sent to San Francisco police.

“It’s interesting, I mean it’s obviously a very famous case here in San Francisco,” said Jeff Harp, a security analyst for CBS San Francisco who worked for 21 years with the FBI, though not on the escape.

The three bank robbers gained widespread notoriety and folklore after escaping from the high-security lockup on June 11, 1962 — the only convicts to successfully break out of the island prison, nicknamed “The Rock.”

In 1979’s “Escape from Alcatraz,” Clint Eastwood portrayed Morris in a dramatization of the trio’s escape. The warden, played by Patrick McGoohan, informed him that no inmate had ever made it out alive.

According to the feds, the men used a homemade drill devised from a broken vacuum cleaner motor to widen vents and crawl through before clambering up a series of pipes.

They eventually made it out through the ventilation system that led them to the prison roof and slid down the smokestack to the ground, where they launched their makeshift raft fashioned out of more than 50 raincoats.

They also created life vests and wooden paddles.

The next morning, shocked guards found dummy heads made of plaster, papier-mâché, paint and real human hair in their cells.

According to the letter, Morris died in 2008 and Clarence Anglin died three years later.

The writer offers a deal: “If you announce on TV that I will be promised to first go to jail for no more than a year and get medical attention, I will write back to let you know exactly where I am. This is no joke…”

The US Marshals Service, the sole agency probing the case, said the FBI lab examined the letter for prints and DNA, KPIX reported. The FBI’s results were inconclusive.

“So that means yes, and it means no, so this leaves everything in limbo,” Harp said.

The letter writer said he lives in Southern California after spending many years after his escape living in Seattle and North Dakota.

In a statement to CBS, the Marshals Service wrote: “There is absolutely no reason to believe that any of them would have changed their lifestyle and became completely law abiding citizens after this escape.”

National Park Service Ranger John Cantwell said: “The Federal Bureau of Prisons say that they drowned once they got off of Alcatraz and their bodies were swept out to the Pacific Ocean — end of story.”

There have been previous tantalizing reports about the escaped prisoners.

A 2015 History Channel special showed a photo allegedly showing John and Clarence in Brazil — 13 years after their escape.

If the men are alive today, Morris would be 90 years old, John Anglin 86 and Clarence Anglin 87.