According to the unpublished third volume of his official biography, the author spent his final years in a blur of constant travel, striving to keep one step ahead of public attention and the depression that dogged him.
Moving around the globe, often incognito, the writer knew little rest and even courted danger, says Norman Sherry, who has spent the past 24 years researching his life.
"Greene became one of the rootless ones," said Mr Sherry, who flew back to his home in San Antonio, Texas, last week to finish the long-awaited third volume of his comprehensive work on the author.
"I have never known anyone travel so much at such a late stage in life. He was constantly escaping, so there is no question of this final book being the study of a decline - the man goes on until his very end and there was no diminution of his powers."
Comparing Greene to Querry, the central figure in A Burnt Out Case, Mr Sherry's book will suggest that the writer deliberately kept up a frantic pace, although he was emotionally a spent force. "He never gave up, though. He burned himself out through thinking hard and living hard," said the biographer, who has himself faced ill health in an effort to complete the trilogy before the new millennium.
"Graham once said to me that he didn't believe he would see the publication of my second volume, and that he did not think either of us would see the publication of the third. I hope I am about to prove him wrong."
Before Greene's death from leukaemia in 1991, he chose Mr Sherry as his official biographer on the strength of his biographical work on Joseph Conrad. Mr Sherry has now completed more than half of the final volume, which covers the period from 1955 up to the author's death, and he expects to deliver the finished manuscript to his publishers, Jonathan Cape, in February next year. Publication is planned for November 1999.
The first 783-page volume of The Life of Graham Greene took 16 years to complete and the second, which came out in 1994, took five. Cape is understandably relieved that the pace has picked up a little.
A spokesman said: "We are very pleased Norman has managed to break the back of it. It has been a long struggle for him and I guess for us too."
Mr Sherry said that, by travelling to Mexico, he was able to unearth, among other discoveries, the truth about the real "whisky priest" behind the central character in The Power And The Glory, one of the author's most famous works.
"My work was much easier in the back reaches of places like Sierra Leone and Liberia. No one passes through these places without leaving tracks," he said.
Greene's widow Vivien agreed that her husband rarely spent three weeks in the same place. Towards the close of his life he had a villa in Capri and flats in Antibes and Paris, but he was often out of reach in further- flung outposts. Latterly, he often went to the Caribbean, either to Jamaica to stay with Noel Coward or Ian Fleming, or else to Haiti. "In Haiti I managed to stay in the very same place that Greene had stayed during Papa Doc's regime. He seems to have thrived on being in danger over there," said Mr Sherry.
"He told me he thought he would go out with a bang and not a whimper. He may have been wrong in the end, but he certainly had reasons to expect a violent death."
Greene's incredible energy was also the explanation for his enduring appeal to women, Mr Sherry argues.
"He was a manic depressive and so when he was in a manic phase he had an immense energy that could be very attractive.
"I found one late letter to his long-term lover Catherine Walston which mentions that he had stayed up late last night and then, in passing, he notes that he is writing at 4.45am."
Mr Sherry has had sole access to Greene's papers and to many letters from his family, lovers and friends.
"I believe there were two kinds of women in his life: those he regarded as a kind of `adventure' and those who were hugely important to him," said the biographer. "Catherine Walston, for example, remained very important to him well into this third section of his life - even once the affair was over."
It was, however, his mistress Yvonne Cloetta (or "Madame C") who shared his life for nearly 25 years and was with him during his final illness.
Deception and infidelity were always at the heart of a man who had learned to be a spy in his youth with the British Secret Service, Mr Sherry concedes, but he robustly defends Greene from the accusations of his rival biographer, Michael Shelden. In his book Graham Greene: The Man Within, Michael Shelden accused Greene of closet homosexuality, mafia sympathies and ultimate literary failure.
"How he can say that about a man who wrote The Comedians?" protested Mr Sherry. As for his own book, Mr Sherry feels volume three may be "the last and the best book I ever write".
"It has cost me a fortune," he explained. "Even if it is a world bestseller, the losses I have made this year would never be recovered. I have worked on unpaid leave for the last six months, but at the end of the day what matters is that I have done the job properly."
And it has certainly been done thoroughly. As Greene's widow herself once pointed out wearily: "I mean, it could all have been in one compact volume. You can do William Blake in one volume, after all."