His ambitions could run further still. These days Oprah Winfrey is shaking the media world by creating not just a show that bears her name but an entire network too. "It would be wonderful to become what Oprah has become: she is in such a class of her own, as an entrepreneur, as a performer and an icon," Rose admits. "The idea of building a series of programmes and choosing people that I think have talent to do them would be a very interesting idea. I would love to show that television can have soul, depth and range."
But how long does he think he can continue to do so? Indignantly, he explains that he maintains his form by running with his dog, Barclay, around Central Park each day. It is very convenient, he adds, since he lives on 59th Street and 5th Avenue.
The waiter appears and removes our plates; he has eaten half of his salad, while I have finished off my (fairly spartan) cod. I order a double espresso; Rose just a regular coffee. Dessert is not even discussed.
So if he could choose three dream guests for the perfect show, I ask, who would they be? He pauses for a long time. "I would love to have a long and serious conversation with the Pope. And Woody Allen, whom I have never interviewed."
There is another long, pregnant pause. "Then, after those two? Steve Jobs," he continues.
My mind boggles at the combination; where would that "conversation arc" go? He laughs loudly and freely, and I notice that the once-packed restaurant has almost emptied; somehow, almost two hours have glided by, seamlessly and unnoticed. And I am still not clear who exactly has orchestrated that.
I ask for the bill, and we walk out. For a second, as he strides down the street in his brown coat, he looks almost anonymous. But when I return to my desk, a colleague tells me that as we sat eating, Michael's has proudly tweeted to the world: "In the house: Charlie Rose and Gillian Tett!" Those electronic sound bites have a way of intruding; even for a man who is trying to take the old-fashioned art of conversation to a new extreme.
This article originally appeared in Financial Times. Click here to read more coverage from the Weekend FT.