In the summer of 1988, during the long vacation from university, I travelled south to Antibes on the French Riviera to try to find Graham Greene. I’d been reading what turned out to be his last novel, The Captain and the Enemy, in which a young boy is hurried away from school and off on an adventure by a mysterious benefactor, as well as an interview with Greene in which he spoke tantalisingly of his life in Antibes. On a whim, I thought it might be exciting to call by at his apartment above the famous harbour, perhaps for afternoon tea. (In the event, I could not find it, but I had fun trying.)

Greene (1904-91) seemed to me then to be an extraordinarily glamorous figure. He was of and formed by the establishment, by public school and Oxford, but seemed contemptuous of it; an Englishman who seemed happiest outside England; a world-famous novelist who refused to appear on television.

He was politically unaligned, claimed by both left and right, but loathed the US, remained close to Kim Philby long after his disgrace and flight to Moscow, and sought out the company of Latin American and Caribbean strongmen. He was an explicitly Catholic writer who professed to be agnostic - and so the contradictions and intrigues multiplied.

Greene occupies an ambiguous space in English letters, suspended somewhere between the Conrad of the ambivalent novels of urban extremism, The Secret Agent and Under Western Eyes, and the John Le Carré of A Perfect Spy and Tinker, Tailor, Soldier, Spy: better than most of his contemporaries and peers, then, but not quite considered to be a great canonical writer. Certainly he wasn’t considered worthy of study at my university, where modernism and postmodernism held sway. Yet his best novels - The Quiet American, The End of the Affair, The Heart of the Matter - have lasted and repay rereading, even if their metaphysical preoccupations can seem portentous and overwrought.

Greene cultivated a sense of mystery, as Pico Iyer reminds us in his elegant new book, The Man Within My Head, which is part-memoir, part-travelogue, and part-extended literary meditation. Greene claimed to be haunted by an avenging double who impersonated him around the world. From “the unknown Graham” is how he inscribed the French edition of The Quiet American he gave to Yvonne Cloetta, his companion of several decades. “You couldn’t really know Greene,” Paul Theroux tells Iyer. “He didn’t want you to.”

For Iyer all the mystery merely enhances the allure of a writer who, from the outset of his writing life, has served as his “shadow associate” and moral guide. But Iyer can be too forgiving of Greene’s cruelties, not least to his first wife, Vivien, from whom he separated in 1948 but never divorced, and to his hapless authorised biographer, Norman Sherry.

Greene once gave Sherry a map depicting all the places in the world he had visited and the poor man was encouraged to shadow his every move, to the ultimate detriment of his health. His three-volume biography of Greene is a study in demented ambition: in trying to tell the whole story of Greene’s complex and itinerant life, Sherry, this purveyor of total biography, ends up lost and confused, endlessly pursuing false leads in some distant land.

Iyer’s approach is more sensible. His book is concise, impressionistic, partial, as much about himself and his family story as it is about Greene (“Was it only through another that I could begin to get at myself?”), and all the better for it.

Born in Oxford, the son of Indian academics who moved to California when he was eight, Iyer was educated at Eton, Oxford and Harvard, and now lives in rural Japan, “the most clarifying society I know”. As a correspondent for Time magazine, that embodiment of bland globalisation, he is an habitué of the club class airport lounge and international hotel, on the move, occupying the spaces in between cultures. He’s a self-described “global soul”, the title of an earlier book, and it’s a feeling of deracinated cosmopolitanism that most attracts him to the worldly and questing Greene.

Iyer writes with charm and intelligence, but he can be grand. “A writer is a palmist, reading the lines of the planet,” he says, in what is less a general statement than a sly self-description. Reflecting on his journey from Eton to his present status as world citizen, he writes: “I sometimes thought that that was what school trained us for - Empire in the post-imperial age, toughing it out abroad ... learning to observe, to read the world, to play at being unofficial spies.”

This is too self-mythologising for my taste. At such moments, Iyer begins to sound like the protagonist of a middle-period Greene novel, the man “living on the dangerous edge of faith” (as John Mortimer once put it), a restless traveller or fugitive adrift in the world, unsure of what or where to call home, and yearning for a greater, deeper truth.

In the end - Iyer grasps this - the insistent message of Greene’s greatest fiction seems to be that there is an infinite amount of hope in the world, but not for the unbeliever. For him, beyond hope, there lies only damnation, in this world and after.