It could rank as the classic rock concert of the century — six bands and performers who revolutionized popular music in the 1960s gathering in the Southern California desert over a single weekend in October.

The company that stages the Coachella Valley Music and Arts Festival is planning a three-night event featuring Bob Dylan, Paul McCartney, the Rolling Stones, the Who, Neil Young and Pink Floyd’s Roger Waters — all Rock and Roll Hall of Fame inductees — Oct. 7-9 at the Empire Polo Field in Indio, The Times has learned.

The six acts have never shared a billing before, and it also would be the first time that Dylan and ex-Beatle McCartney — representing what are widely considered the two most important rock acts of the 1960s — have played on the same bill, albeit on different nights.

The concert is being organized by Goldenvoice, the Los Angeles-based promoter that is a unit of AEG Live, according to people with knowledge of the plans. They could not speak publicly because negotiations with the performers were being finalized.

“It will be their full stage productions, with full sets,” said one person close to the project. That would be in contrast to most festivals that have bands typically playing abbreviated sets.

Plans are nearly complete, and an official announcement is expected in coming weeks.

“It’s so special in so many ways,” said Young’s longtime manager, Elliot Roberts. “You won’t get a chance to see a bill like this, perhaps ever again. It’s a show I look forward to more than any show in a long time.”

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Under the tentative plans, Dylan and the Stones would play back to back on Oct. 7 to open the festival. They would be followed on Oct. 8 by Young and McCartney and their touring bands.

The event would conclude on Oct. 9 with the Who and Waters, the former Pink Floyd bassist, songwriter and singer.

“If you just look at it at face value, a bill like this doesn’t exist anywhere else on the concert landscape,” said Gary Bongiovanni, editor of the concert-industry tracking publication Pollstar. “There are a lot of festivals, but nothing quite like what’s being planned there. I expect it will resonate nationally — and internationally.”

The concert would gather in one weekend six of the biggest names in rock, musical prime movers who didn’t just redefine the parameters of rock music but transformed it from teenage entertainment into an art form. In many cases, their songs also served as the soundtrack to the social and political upheaval of the 1960s, ’70s and beyond.

They put their parents’ generation on notice that the times they are a-changin’, empathized with all the lonely people and seductively exhorted peers to spend the night together. They bragged to authority figures that we don’t need no education, taunted that they hoped to die before they got old and suggested that it’s better to burn out than to fade away.

The festival would also constitute yet another sign of Goldenvoice’s continued evolution beyond its beginnings in the early 1980s as a scrappy grass-roots promoter that organized punk-rock shows in low-rent theaters, warehouses and other off-the-grid venues in Los Angeles, Orange and Riverside counties.

The company’s flagship event, the Coachella festival that began Friday, has become the best-attended and highest-grossing music festival in the world — with attendance at 99,000 a day over six days.

Coachella’s six-day gross of more than $84.3 million last year dwarfed the competition, according to Pollstar, the concert industry-tracking publication.

Although the festival has it roots in alternative rock, organizers have increasingly tipped their hat to rock’s old guard — and crowds have responded with enthusiasm to appearances by McCartney, Waters, AC/DC, Steely Dan and other classic-rock acts. That suggests the fall festival could find an audience beyond the baby boomers who grew up with ’60s and ’70s rock.

All the participating artists have strived over the years to remain relevant, often expressing greater interest and passion toward their latest creations than revisiting past glories.

Separately, the Stones, McCartney, the Who and Waters typically put on among the highest-grossing concert tours whenever they go on the road, usually appearing in sports arenas and stadiums.

Dylan usually plays in midsize theaters and amphitheaters of 3,000 to 10,000 capacity, and Young habitually shifts formats from acoustic to electric and solo to group settings, performing in recent years in venues as small as the 3,400-seat Dolby Theatre in Hollywood on a solo tour to the 17,500-capacity Hollywood Bowl with his band Crazy Horse in 2013.

Beyond whatever paychecks they’ll get out of it, the featured performers have the allure of a prominent role at a likely never-to-be-repeated gathering of rock music titans.

Where most festivals schedule dozens of acts performing across multiple stages, the new festival is expected to use just a single stage in the northeast corner of the polo field’s grounds.

Some of the show’s participants have performed together previously — Dylan and the Rolling Stones shared bills in South America in 1998 and even teamed up at one point for a version of Dylan’s 1965 rock classic “Like a Rolling Stone,” while McCartney, Waters, the Who and Young have appeared with one or the others at large-scale benefit concerts.

Of the four English acts on the bill, McCartney — as a Beatle — appeared on occasion with the Stones or the Who, but only early in their careers and even then, very briefly — those bands quickly playing just a song or two for television or radio programs. Waters and Pink Floyd emerged after the Beatles stopped touring in 1966.

Record producer-engineer Glyn Johns, who worked with both the Beatles and the Stones in the late-’60s, wrote in his 2014 memoir “Sound Man” that Dylan once approached him in the late-‘60s to explore whether England’s two biggest rock bands would be interested in recording with him, a rock Valhalla-like summit meeting that never came to fruition.

Dylan famously played with George Harrison in 1971, shortly after the Beatles broke up, when Harrison organized the Concert for Bangladesh benefit at Madison Square Garden in New York. That pioneering benefit concert also featured a bevy of other rock stars including Eric Clapton, Leon Russell, Ringo Starr and Billy Preston.

Dylan, McCartney, Mick Jagger (minus the rest of the Rolling Stones), the Who and Young all appeared in 1985 for the Live Aid series of benefit concerts, which played across two continents.