The former's frontman, Dave Grohl, was previously inducted into the Hall of Fame as part of Nirvana in 2014, but it's the first time Foo Fighters have been nominated.
And the 'Learn to Fly' hitmaker has revealed he would like The Police drummer Stewart Copeland to induct the band should they be chosen to enter the Hall of Fame, because he inspired him to start Foo Fighters as a solo project after Nirvana dissolved in 1994.
He told Howard Stern on his SiriusXM show, he recalled: "One of the reasons why I did that is because when I was young someone gave me a record by an artist named Klark Kent, right?
"It was this kind of weird, fringe thing. Klark Kent? Who's Klark Kent? It sounded a lot like The Police. It sounded a lot like The Police, because it was actually Stewart Copeland. The drummer of The Police made this record under the name Klark Kent. He didn't put his name on the record."
Dave added: "If you've ever hung out with Stewart Copeland, he can make a f****** speech."
As for Carole, she was previously inducted as a songwriter along with Gerry Goffin in 1990.
Tina Tuner is also up for the honour and had been inducted in 1991 with Ike Turner.
Rage Against The Machine have also received their second nod, having previously being nominated in 2019.
LL Cool J has been nominated for a sixth time, while it's Chaka Khan's third time as a solo artist.
Other nominees included Kate Bush, New York Dolls and Todd Rundgren.
John Sykes, chairman of Rock & Roll Hall of Fame Foundation, commented: “This remarkable ballot reflects the diversity and depth of the artists and music the Rock and Roll Hall of Fame celebrates. These nominees have left an indelible impact on the sonic landscape of the world and influenced countless artists that have followed them.”
The class of 2021 will be unveiled in May.
The 2020 ceremony, which was held virtually amid the COVID-19 pandemic, saw the likes of Depeche Mode, Nine Inch Nails, The Notorious B.I.G., T. Rex, Whitney Houston and The Doobie Brothers honoured.