But less attention has been paid to the bass player they were trying to recruit: Paul McCartney, who was busy with another band at the time.
This tantalizing detail about the super group that never was jazz standout Tony Williams would have been on drums is contained in an oft-overlooked telegram that Hendrix sent to McCartney at The Beatles' Apple Records in London on Oct. 21, 1969.
"We are recording and LP together this weekend," it says, complete with a typographical error. "How about coming in to play bass stop call Alan Douglas 212-5812212. Peace Jimi Hendrix Miles Davis Tony Williams."
The telegram, advising McCartney to contact producer Douglas if he could make the session, has been part of the Hard Rock Cafe memorabilia collection since it was purchased at auction in 1995. Still it has only generated attention in recent months with the successful release of "People, Hell & Angels," expected to be the last CD of Hendrix's studio recordings.
"It's not something you hear about a lot," Hard Rock historian Jeff Nolan said of the telegram, now displayed at the restaurant in Prague. "Major Hendrix connoisseurs are aware of it. It would have been one of the most insane supergroups. These four cats certainly reinvented their instruments and the way they're perceived."
French promoter and Hendrix fanatic Yazid Manou, who has researched the telegram, says it offers a glimpse of what might have been.
"It's amazing because of the names of the people," he said. "Of course that didn't happen, but the telegram brings us something to dream about. This is a document, proof that they had an idea to do an album."
The telegram raises more questions than it answers. It's not clear if McCartney was even aware of the unusual, apparently impromptu invitation to rush from his London base to New York for the planned session.
Beatle aide Peter Brown replied on McCartney's behalf, telling Hendrix the following day that McCartney was on vacation and not expected back for another two weeks.
The invitation came at an extremely awkward moment for the Beatles' bassist. It was sent the same day a prominent New York City radio station gave wide exposure to a rumor that McCartney had died in a car crash and been replaced by a lookalike. The bizarre story, supposedly supported by hints on Beatles records and album covers, briefly gained worldwide credibility. Its dark nature apparently prompted the exasperated McCartney to retreat with his family to their farm in Scotland.
It also came at a time when the Beatles were falling apart due to business and artistic conflicts that likely would have been exacerbated by McCartney appearing on a record with Hendrix and Davis. McCartney was also still bound by a songwriting partnership with John Lennon that might have further complicated the release of any McCartney-Hendrix-Davis compositions.
And then there is the question of what the proposed group would have sounded like. Davis was moving away from his jazz roots toward a fusion-based sound. He said in his autobiography that by 1968 he was listening primarily to James Brown, Sly and the Family Stone and, particularly, Hendrix musicians joined by a love of syncopated funk not found on Beatles' tracks.
It is not clear either how McCartney's melodic, subtle bass playing would have made its presence felt in a band that included Hendrix' guitar and Davis' trumpet.
"At first, though, it sounds really weird and off the wall. But on second thought it makes perfect, Hendrix-type sense to chuck in someone who's a great musician but comes from a different tradition," said Hendrix biographer Charles Shaar Murray. "I regret this never actually took place. ... it would have been magnificent."
McCartney is the only one of the four musicians who is still alive. His spokesman, Stuart Bell, said the former Beatle is too busy on his world tour to comb his memory for his thoughts about a telegram sent more than four decades ago.
In his autobiography, Davis said he and Hendrix occasionally jammed together at his apartment in New York City and tried to get into the studio to record but were hampered by financial matters and by their busy schedules. Murray and others maintain that Davis wanted $50,000 up front to attend the session.
The Juilliard-trained trumpeter Davis described Hendrix, who learned his chops backing up the Isley Brothers and others, as a self-taught "natural musician" who could not read music but was able to pick up complicated pieces in the blink of an eye.
Davis says in the book that he and arranger Gil Evans were in Europe planning to record with Hendrix at the time of his death in London.
"What I didn't understand is why nobody told him not to mix alcohol and sleeping pills," Davis wrote.
Hendrix's death dashed their plans to record together, with or without McCartney. Eddie Kramer, the engineer who produced most of Hendrix's music, said there will always be speculation about what might have been.
"I think it would have been phenomenal," Kramer said. "Lord knows where it may have gone; those huge egos in the studio at the same time! I would have loved to have done that one. But it was not to be."