The band have received six nominations for their second album Babel including best rock song and album of the year.
Jay-Z, Kanye West, Frank Ocean, Fun and The Black Keys are also up for six awards.
Babel is the second biggest-selling album in the US this year behind Taylor Swift's Red, which was ineligible for nomination because of its later release date.
The winners will be announced in a televised ceremony on 10 February from Los Angeles.
Jay-Z and Kanye West are jointly nominated for their album, Watch The Throne.
It includes a best rap performance nod for their track Paris.
Grammy Awards: See a list of selected nominees
Kanye West also has multiple nominations for his song Mercy, while Jay-Z is also recognised for his collaborations with Young Jeezy and Rihanna.
Both Rihanna and Kelly Clarkson picked up three nominations and will be competing with each other in the best pop solo performance category for Where Have You Been and Stronger (What Doesn't Kill You) respectively.
Kelly Clarkson, Frank Ocean and Taylor Swift are up for record of the year
Record of the year nominees see an assortment of rock, pop and hip hop nominees, with Clarkson's Stronger up against The Black Keys' Lonely Boy and Fun's We Are Young.
Also in that category is Gotye with their hit Somebody That I Used To Know, Frank Ocean and Thinkin Bout You and Taylor Swift's We Are Never Ever Getting Back Together.
To be eligible for nominations this year, artists had to release their music between 1 October 2011 and 30 September 2012.
Adele, who dominated last year's awards with six got only one nomination this year for best pop solo performance, as she did not release any music in the time frame.
The nominations for the main categories were announced in an hour-long television programme hosted by Taylor Swift and LL Cool J.
Other British nominees include Ed Sheeran, Calvin Harris and Florence + The Machine, as well as The Who, who will receive the Grammy lifetime achievement award.
Ed Sheeran wrote on Twitter: "A team. A song I wrote with no home, no money, anything, nominated for best record at the Grammys. A dream come true. Ecstatic xxx."
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