"It must be strange being in a room, in front of all these people when they're listening to your music and seeing and hearing their reaction," offers Cocker as an opening gambit.
"Oh, it is. But I'm testing it, to see if it finds favour with the audience and also with myself," Cohen teases. "I have to say I've been pretty swept away with it and the reaction to it. But then I think this particular record invites you to be swept away - even if you have no rhythm yourself."
It does sweep you away, because it's an intimate, semi-autobiographical album. Songs like the opening track, Going Home, where Cohen chastises himself for his faults, Show Me The Place and Crazy To Love You entice you in with their simple, evocative mix of the holy and profane, the cerebral and the carnal - themes that habitually reprise themselves throughout his richly woven tapestry of songs.
"I never had any kind of strategy to do that," admits Cohen. "And I've never felt a sense of abundance with my writing. If anything, it's the opposite: I've always felt I was at the end of the line, scraping the bottom of the barrel just trying to get the song together and come up with a beginning, middle and end.
"There are people who work with a sense of abundance but sadly I'm not one of them," he adds, sighing. "I've never had a sense that I was standing in front of a buffet table with a multitude of choices. I just try to piece something together and now and then, by some grace, something stands out and invites you to work on it more. It's a mysterious process, which depends on perseverance, perspiration and also a certain amount of grace and illumination."
It's a surprising admission from one of music's most respected lyricist and poets, as recognised by his Grammy Lifetime Achievement Award and induction into the Songwriters' Hall of Fame, in 2010. But his admission partly explains the often lengthy periods between his albums and the eight-year hiatus since his last record, Dear Heather, and new collection, Old Songs.
"It didn't seem that long. It just seems like yesterday," shrugs Cohen. "I certainly never feel like I've stopped writing, or there's been a break because I pretty much work at this every day.
"I understand from the outside that it can look like I'm not doing much, because nothing appears in the shops for a while. But, believe me, this workshop never shuts down," he asserts, tapping his temple. "Part of the delay is I find it very hard to abandon a song until I've polished it and brought it to as close a finish as I can. Only then do I feel I can discard it if it's not working.
"That's what happened with Hallelujah, which took me over four years to write. I wrote so many verses for it but I couldn't throw any of them away until I'd made each one the best it could be. Only then did I discard any," he clarifies. "That's a time-consuming process, which is why it takes me a long time to finish an album."
Ironically, it could have taken Cohen even longer than eight years to write Old Songs, had it not been for a tour of his previous album. That tour was originally scheduled for a few shows but snowballed into a two-year, 246-date marathon run, which reignited his passion to perform live.
"That tour really reinvigorated me, in the sense of being touched by the reception of all the people across the world," he concedes, smiling. "I'm not insensitive to that appreciation, so that did have an invigorating effect.
"I'd kind of forgotten what it was like to tour, because I hadn't done anything for 15 years - it was like being Ronald Reagan in his declining years, where he remembered he once had a good role, playing a President in a movie," Cohen jokes.
"I felt a similar thing: that I had once been somewhat a singer. But being back on the road really re-established me as a worker in the world and that was a very satisfying feeling.
"So, when I finished the tour, I didn't feel like stopping because I felt energised by what went on during that tour. Consequently, I wrote this record."
Perhaps that momentum will carry over into yet another record and a new tour? But we'll just have to wait and see if that happens ..."