"Despacito" is also nominated for song of the year - a songwriter's award - along with Mars' "That's What I Like", Jay-Z's "4:44", Logic's "1-800-273-8255" and Julia Michaels' "Issues".
For album of the year, Jay-Z and Lamar face Mars' "24K Magic", Childish Gambino's "Awaken, My Love!" and Lorde's "Melodrama".
The nominations for The 60th Annual Grammy Awards have been announced today and in the category of "Best Musical Theater Album", the nominees (in alphabetical order) are.
The 60th Grammy Awards, music's biggest night honoring the year's achievements across more than 80 categories, are scheduled for January 28 at New York City's Madison Square Garden.
"Despacito", the hit from Puerto Rican singer Luis Fonsi featuring Justin Bieber and Daddy Yankee landed three nominations including record and song of the year.
Paintsville, Ky., native Chris Stapleton, who won two Grammy Awards in 2016, including Best Country Album, was nominated for Best Country Album again for "From the A Room, Vol. 1".
Other artists with multiple nominations included: Kendrick Lamar with seven, Bruno Mars with six, Childish Gambino, No I.D., Khalid and Sza all with five nominations each. Those voting members, who number around 13,000, are "professionals who listen objectively to music and make a judgment", he added.
While the obvious Grammy prediction would be Bruno Mars, it would be a shame not to see a rap album win the award. Neither released new music this year.