On Friday, the 50th anniversary restoration of Lawrence of Arabia was released on Blu-ray. And later this week, Sharif arrives in London to attend a party for the film's costume designer to be held at the V&A.
It was the film that launched him as a leading actor — in the ensuing decades, his name would be linked to a string of women including Barbra Streisand and Anouk Aimee — yet when I recount the tale of his fan from Dallas, those famous eyes scrutinise me in mock horror.
It's a potential game-over moment. But then the stories start to flow. Despite his protests, there's clearly an impressive resilience about the mind and, indeed, the body that first came into the world in Alexandria, Egypt, in April 1932.
As an octogenarian, Sharif still possesses that lean, almost angry beauty that marked him out first as a promising Egyptian film star, and then, following his discovery by David Lean, an international screen idol.
All the attributes that were there in his youth remain — the cheekbones like ridges along cliffs, the taunting imperfection of the gap-toothed smile, those eyes whose glittering fury was captured so strikingly by Lean in the scene from Doctor Zhivago where he watches the Cossacks slaughter peaceful demonstrators.
It takes a certain arrogance to pull off this statement at any age, and Sharif certainly isn't lacking in self-belief.
Despite the rebelliousness and towering ego, Sharif seems extremely malleable when it comes to those he respects.
Take the famous — some might say defining — moustache, which wasn't his idea at all, but David Lean's. "I was taken in a plane to the desert to meet David," he relates, "and as we came in to land we could see him sitting all by himself.
We landed right next to him, but he didn't move one step. When I got off the plane, he didn't say 'hello'. He simply walked round me to see my profile. Finally, he said 'That's very good, Omar. Let's go to the make-up tent.' I tried on a moustache, and it was decided I would grow one.
I've shaved it off for a couple of films, but otherwise I've had it ever since."
The man who was born Michael Shalhoub has always lived at the heart of the action, even in his own country. His father, a prosperous timber merchant, increased his wealth when he salvaged barbed wire left behind by the British during the Second World War in the desert, and turned it into nails. As a result, the family moved to an area in Cairo where they soon came to King Farouk's attention.
"My mother used to play cards with King Farouk," Sharif declares. "He believed she brought good luck to him — she was his mascot. He often came round to our house. I was around 10 years old at the time — if I came home and realised he was there, I would just sneak into bed.
My mother used to sit up all night." He laughs. "By night she would play cards, by day she would give me the slipper. She hit me on my backside every day till I was 14. She was an extraordinary woman — she lived till 1998. I was very close to her, even though she beat me all the time!"
Certainly the love of cards, despite the beatings, has proved a central dynamic in Sharif's life. Famously, he was one of the world's top 50 bridge players — the Omar Sharif Bridge Circus played exhibition matches all over the world — and he once received a late-night invitation to play with the Shah of Iran and his wife.
Does he play now? "No," he says soberly. "I stopped six years ago when I stopped being good enough."
After his marriage to the Egyptian movie star Faten Hamama collapsed during the filming of Doctor Zhivago — "She was the love of my life," he asserts — he has lived what has seemed, especially in recent years, to be a solitary, unsatisfactory existence. "From the age of 31, I have lived in hotels," he says.
"He is a law unto himself — though he tells me happily that he's going to see his family (he has one son, and a number of grandchildren) in Cairo at the start of next year.