Is Bill Frisell the best jazz guitarist in the world? There is some snazzy opposition - from the melodious Pat Metheny to the frenetic John McLaughlin. You could say he is the most in demand - and from way beyond jazz. Frisell's limpid tone has backed Elvis Costello, Marianne Faithfull and David Sylvian. He has rocked out with Ginger Baker; he's there on Paul Simon's last CD, and Norah Jones's. His own 30-plus albums run the gamut from country, bluegrass and Americana to industrial squeaks and shrieks.

But the last person to give a proper assessment of Bill Frisell's diverse genius is Frisell himself. He fixes me with a grin and in his sing-song Midwest tones says: “I guess I've been really lucky. There's always been these opportunities that are just always there for me. I seem to run into people and they want me to play. Something will just present itself.”

Frisell, 57, is a one-off. In a world in which electric guitarists are typecast as Jack Daniels-fuelled Slash-alikes, Frisell is a pastel-shirted introvert. He may bend notes like Hendrix but he looks like Bill Bryson (the difference is that Bryson talks a lot). Back home in Seattle, friends call him Clark Kent - the mild man with supernatural digits.

He grins. “The whole time I played in rock bands I was always criticised because I didn't move around. But it was always about the music with me. I'm not into the showmanship part. The music is in my head. I can get wild in there.”

At the London Jazz Festival in November his trio is going multimedia, playing original compositions to a collection of short films, some by his cartoonist friend Jim Woodring, others by Buster Keaton, plus the artist Bill Morrison's hallucinatory reconstituting of The Mesmerist, a 1926 film slowly being destroyed by nitrate deterioration. Frisell likes the challenge of playing to images. “It almost corners me in a certain way. I have to think of things that I wouldn't normally do, so I find myself growing somehow.”

It's only his second British date of a packed working year. That previous show was at the Cheltenham Jazz Festival in May and - as at the Barbican next Saturday - he played no music from his latest album, the delightful History Mystery. Not for Frisell the soul-sapping slog of tours to promote the new “product”. “I have a pretty amazing situation with my label [Nonesuch] where I can do what I want. I know they wish things would sell more but I've never felt that kind of pressure.”

Thus Frisell has recorded soundtracks for Buster Keaton movies; he covered Charles Ives and Madonna on Have a Little Faith; and recorded the music for a remake of Psycho in his bedroom. He made a soundtrack for animations by the Far Side cartoonist Gary Larson (another Seattle chum and amateur guitar partner). The smart funk of Unspeakable won him a Grammy in 2005. Compare that with making the same Rolling Stones album every three years.

Frisell grew up in Denver playing the clarinet, but two things happened. “Like so many people I saw the Beatles on The Ed Sullivan Show and it was like, maan!” An unassuming school student, his popularity was boosted by a talent show. “I played a Wes Montgomery piece for these girls who were doing a modern dance thing. The whole school went crazy and I became a big star.” Behind his owlish specs his eyes twinkle.

His talents took him to Berklee College of Music to study arranging and composing. He then became a professional musician because, as Frisell puts it, “it was the only thing I knew how to do. I almost didn't have a choice.”

There was the usual start in Top 40 bands and at wedding gigs, but when Pat Metheny recommended him to the veteran drummer Paul Motian, his career took off. “He wanted me for what I could do as a player, not just to fill a role.” During a brief period living in Belgium, Frisell met his wife, Carole, a painter, while she was waitressing in a jazz club. They have one grown-up daughter.

Today the musical meetings continue. A few years ago Frisell got a call out of the blue from Paul Simon's people. “I guess he had been listening to my albums and liked what I was doing. I went to his apartment - this amazing, beautiful place - and we had a day of playing and talking about music. After that I played a little on the Surprise album.”

Who would Frisell like to get a call from now? “Wayne Shorter, Sonny Rollins, Bob Dylan... Dolly Parton.” (He loves her version of Knocking on Heaven's Door recorded with Ladysmith Black Mambazo.) He is also a big fan of Lucinda Williams, the American country/rock singer. “When I played with her I could really play what I wanted to play - and she really responds.”

Meanwhile, Frisell has his own gigs to attend to. Last year he was on the road for 200 days; this year has “gotten a little crazy”. Bob Dylan once said that an artist needs to be “in a constant state of becoming”, and Frisell is a case in point. His trademark guitar sound - those sustained notes that hang shimmering in the air - has slowly developed over the years. “It has come from listening to saxophone players and trumpet players - trying to get the notes to feel as if they had breath going through them.”

The records, too, are never quite definitive statements. “It's in the nature of music that nothing feels like it is finished anyway. I do an album and it's the best I can do at the time. It never feels like you get it completely right.” He grins his faraway grin and drains his glass of water, and the best jazz guitarist in the world (possibly) seems happy to keep trying.

Bill Frisell, Music and Film, Barbican, London EC2, Saturday

History, Mystery is out on Nonesuch

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