"I don't often talk to journalists, but I want to tell you about a conversation I had recently with Bashar," Vladimir Putin tells me, as we cruise above the Siberian tundra in a luxurious private jet. The Russian president pours me an ice-cold vodka shot from a solid gold decanter, and begins his tale. This is absolute dynamite, I think to myself. Nobody gets this sort of access to Putin, and here I am being fed the inside story. Wait until London hears about this!

And then I wake up.

Yes, I dream about Putin. Not that kind of dream, of course, though after a few too many drinks one female correspondent did admit to having such a nightmare, before vehemently denying she had said anything of the sort the next morning. No, in my nocturnal visitations, Vladimir Vladimirovich is fully clothed and opining on matters of state importance.

Part of the reason, I think, is the fact that getting access to Putin is so damn hard, and real-life face time with the man so tantalisingly elusive. In six years as a foreign correspondent in Moscow, the most intimate interaction I have had with Putin was taking part in his set-piece press conferences, attended by over a thousand journalists, all baying to ask questions (many of them along the lines of: "Vladimir Vladimirovich, just how do you manage to be so amazing?").

We Moscow correspondents write so many column inches about Putin, but have to make do with second- or third-hand information, through the anecdotes of those few people around him who do occasionally talk to journalists, or from analysing his television appearances and pithy aphorisms.

Asking around, I soon realised that I am not the only one whose subconscious makes up for the lack of real access to the Russian president by conjuring night-time visions. Putin visits almost every foreign correspondent in their sleep.

One foreign television producer of Russian origin says Putin is a frequent guest at imagined family dinners in her household: "We look at each other across the table, and there is a lot of tension, as we both wait to see whether we can find a common language," she says. "Sometimes he walks off. It's a moment of rejection and I understand I will not be accepted by him ever."

"I dreamed once that Putin was hosting a party to teach us how to drink vodka," Veronika Dorman, a French newspaper correspondent based in Moscow, told me. "There were only pickles on the table, and Putin was saying: 'Let's learn how to drink like real men.' Then we all got on little planes and had to fly through Moscow. The only way to get out of the plane was to crash it. I decided it was better not to analyse any of this."

A Dutch reporter has recurring Putin dreams. "I'm at a press conference and I work up the courage to go up to him and ask a question. He gives me a fatherly pat on the shoulder, and says: 'The thing you should know, is …' But when I wake up I can never remember what he said."

Putin's real public appearances can often be so surreal that they have a vaguely dreamlike quality to them. The Russian journalist and novelist Marina Akhmedova told me she dreamed "of Putin as a huge goose in a tailcoat, flying through the sky, and I couldn't work out if he was wearing shoes or if he had big flippers." Not long after, she was disturbed to see the real-life Putin on television screens dressed in white and piloting a microlight, leading a flock of rare cranes in migration.

The only journalists who get close to Putin regularly are the "Kremlin pool"; the state TV crews and a few print journalists who follow the leader's every move. They spend hours on planes and buses, travel thousands of miles across the world, and while away whole days waiting for the famously tardy president to show up to functions. But even they rarely get the chance to interact with him personally.

I got talking to one state television journalist who has spent time in the Kremlin pool. It turned out that he too was suffering from political visitations in his slumber, but for him it was not Putin who came to him in the dead of night.

"I have this recurring dream," he told me, looking visibly troubled. "It's always the same. I dream about Navalny."

Alexei Navalny is Putin's nemesis, the anti-corruption investigator, leader of street protests and Russian nationalist, whose following is small but who the Kremlin justifiably fears could grow into a serious threat in the coming years. Putin seems to have a pathological fear of saying his name in front of television cameras, using bizarre constructions such as "certain people", or "this gentleman". Navalny is rarely mentioned on state TV, but this apparently does not stop the reporters from seeing him in their dreams.

"So we're chilling out together, Navalny and me, having a great time," said the correspondent. "We're hanging out like two good friends. Usually we go to the cinema. We're getting on like a house on fire. Then at some point he asks me where I work and I have to tell him the name of the channel I work for, and he is absolutely disgusted and storms off.

"And then I wake up."