The late Unchain My Heart singer, who died aged 70 in 2014, is among the nominees for the 2025 class of inductees, and The Beatles legend has backed the Woman to Woman star in a letter to the Rock Hall panel.
"Joe was a great man and a fine singer whose unique style made for some fantastic performances," he wrote, according to Billboard.
"He sang one of our songs With a Little Help From My Friends, a version produced by Denny Cordell which was very imaginative...
"And whilst he may not have ever lobbied to be in the Hall of Fame, I know he would be extremely happy and grateful to find himself where he deserves to be amongst such illustrious company."
The Hey Jude icon is a two-time member of the Hall of Fame, having first been inducted as a member of the Fab Four in 1988, before being honoured 11 years later as a solo artist.
Cocker is a first-time nominee, alongside 13 other icons of music.
He's on the shortlist with Oasis, Joy Division/New Order, Cyndi Lauper, Outkast, Soundgarden, The White Stripes, Billy Idol, The Black Crowes, Bad Company, Mariah Carey, Chubby Checker, Mana and Phish.
Artists become eligible for nomination 25 years after the release of their first commercial recording, and voting for the 2025 inductees has already opened.
The finalists are due to be revealed in April, with around half of the nominees set to be inducted later in 2025.
Liam Gallagher, the lead singer of Oasis, previously rubbished the Rock and Roll Hall of Fame, saying he doesn't crave recognition from "some geriatric in a cowboy hat".
Liam, 52 - who has also enjoyed success as a solo artist - told The Sunday Times newspaper: "I've done more for rock'n'roll than half of them clowns on that board, so it's all a load of b*******."
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