"It's happening," Sjoerd told me. "But I'm afraid I can't be very specific about the details. That's the beauty of the process."
The couple have been plying their trade in the same spot since around the time food was invented. The Middle East, which opened in early May 1980, was a venture by a bunch of new arrivals from the Netherlands who decided to make the kind of cafe they were used to back home.
"In the beginning I was only in charge of advertising," says Sjoerd, "but in time people went their own ways and Marjan and I were left holding the baby."
Surprisingly, perhaps, they have spent no time in the region the eatery is named for, except for a stopover in 45C in Dubai on the way over. Rather, the food they serve is the kind that Lebanese and Egyptian immigrants made in Holland. It's Middle Eastern food slightly tweaked for European palates rather than country-of-origin authentic.
"This food was very popular in Holland at the time," Sjoerd says. "It's changed a bit since - you see more combination shawarma-and-pizza places now and the menus can get huge but when that happens, the quality can suffer.
"We have always tried to do what we do as well as we can. We've never changed the menu, so we have a set system and can do things very quickly. That's what has allowed us to carry on as long as we have.
"But you really feel it in your joints, all the rushing around. This kind of work is better for someone younger."
I tried to calculate how many times I'd eaten at the Middle East. Three shawarmas per film festival gets me over the ton, I reckon, but there will be regulars who would deride such inconstant patronage.
When they expanded into a back room about nine years ago, it eased the standing-room-only jostling that made for a jovial atmosphere, but it was easier to browse the images on the wall, that range from Frank Womble's zany tailor-made oils on board to the kitsch tinted pictures of Bedouins on desert ridges - wartime souvenirs that had ended up in second-hand shops or on Trade Me.
And the camels. Dozens, even hundreds from one to 30cm high: "That was my thing, I have to confess," Sjoerd says.
"I used a camel in an ad that I made and then I saw one in a jeweller's - a crystal paperweight in the form of a kneeling camel. It started from there and I found the others - left, right and centre."
He has no idea how many there are: "People often say we should have a competition to guess but it would never be accurate. Stuff gets stolen. There are a few people around town who have a camel from the Middle East."
Whether the camels will stay is also up in the air, though it's hard to imagine the place without them. Likewise it's hard to imagine it without Sjoerd and Marjan.
"The idea of not having to think about it is great. It will be quite interesting to see how I react to not having anything.
"But when it comes to saying goodbye, you're only as good as your last shawarma."