"I first met him in 1973. He heard my show and was sitting there and I got pulled into a booth by the guy that ran The Bitter End, who was a friend of Dylan's. Now, I'd heard Dylan was in the house that night but I thought he'd got up and left. But he hadn't. So then I'm in this booth across the table from him and he's wearing a coat and a big fur hat, shades and these leather gloves. I mean he looked like a statue! So I extended my hand, as you do, but he didn't take my hand, and then his fingers in these leather gloves just sort of twitched!"
Browne laughs at the memory and continues.
"So I pulled my hand back, said "hello" and split, cos it wasn't like I was invited to hang around. I was brought over just to meet him. I met him another time, a bit later, with Leon Russell and they were up in a hotel room singing songs and drinking whiskey and that was good - but still it wasn't like meeting a person - this guy was like my idol - so it was... ummm... mystifying. I've met him many times now and it's always interesting. But it's like that line he has - "nothing is revealed".
Would you count him as a friend these days?
"No. He's an acquaintance. But he's a hero to me. I think about all the other writers who I love and admire; people like Warren Zevon, Tom Petty, Randy Newman, Steve Earle, Lucinda Williams, Shawn Colvin, Patty Griffin - all of them great songwriters. I mean I would hate to live in a world without any Warren Zevon songs! I completely love all their work - and to think they were able to do it in a world where Bob Dylan has already written most of the great songs!"
On the phone from Sydney - where he's soon to play BluesFest and a gig at the Sydney Opera House - Browne is garrulous and relaxed. Despite telling me he shouldn't talk so much to save his voice he keeps talking - and laughing. Our 20 minute interview soon stretches to 45.
In conversation Browne is anything but the insular, melancholic artiste the public imagines.
"Oh, that's a big misconception," says Browne. "I'm not melancholy at all, but I like sad songs. I like songs that describe life's sorrows, because that's how you get through it. Songs that take you from one place to another."
Somehow the discussion turns to the late, and irascible, Lou Reed.
"Oh a friend of mine Ignacio Julia has just written a book about him. I know Lou Reed had this reputation as a very difficult guy but he was very kind and generous to me.
"I met him when I was working on Nico's record in 1967. All the guys from the Velvets had been accompanying her - getting her solo career up and running - and I ended up getting the job. Lou and I happened to be in the studio on the same day, Lou playing on the songs he did and me playing on mine. And on that day Lou invited me to go with him to see this Murray K show. Murray K was a DJ in New York at the time. I remember it vividly. It was at the RKO Theatre which seated maybe 2000 people - I mean, I can't even believe the bill - Creem, The Who, Wilson Pickett - it was incredible - and I'm there sitting in the balcony with Lou Reed!"
Browne's hit album Running On Empty (1977) contained classic songs about life on the road. But touring life is different now.
"Back then we didn't sleep. We smoked and drank, did all that stuff," he says.
"These days on the road I keep to myself, I read, exercise and listen to music and play guitar. I don't go anywhere or talk to anybody. Cos I can't really sing the way I want to sing and talk a lot. It's more of an issue now than when I was young, but then I sing better now than when I was younger.
"These days I live in a more sustainable way and you have to because a lot of the people I knew then aren't around anymore."
"My anti-ageing tip is - "don't be stupid"! I try to eat well... actually for a while I even took a chef on the road and that was great but it turned out to be too expensive."
Browne can't quite recall if it's his third or fourth visit to New Zealand.
"Actually I was in Auckland just last year, I wasn't playing but just supporting the Polynesian Voyaging Society's navigation project. They're amazing people who're sailing a Polynesian voyaging canoe around the world purely by celestial navigation."
At the Civic Browne will be playing with his six-piece band - including in-demand guitarist Greg Leisz - who contributed some stunning work to Lucinda Williams' recent albums.
"I love playing Auckland," says Browne.
"Actually I love Auckland even when I'm not playing there! And I love this band. I think it's my best band and to be down in this part of the world and to get to play is a real thrill for all of us."
Jackson Browne performs with his band on April 3 at The Civic Theatre. For complete tour and ticketing details, visit: www.livenation.co.nz.
Greg Fleming is an Auckland-based writer and musician. You can follow him on twitter