Young Man With the Big Beat: The Complete '56 Elvis Presley Masters, a collection of the singer's early material, is up for the top prize in the 'Best Historical Album' category.
Sir Paul McCartney and Chris Strachwitz are among the other artists nominated for the gong by the National Academy of Recording Arts and Sciences.
Presley, often referred to as the King of Rock 'n' Roll, earned 14 Grammy nominations and three wins during his musical career. He passed away in 1977 from cardiac arrest at the age of 42.
Eric Bana is to portray the singer in Cary Elwes's forthcoming movie Elvis & Nixon, scheduled for release next year.
The Grammy Awards will take place in Los Angeles on February 12, 2012.
> Alice Cooper: 'Elvis asked me to shoot him'
Watch Elvis performing 'Young Man With the Big Beat' below: