Cooper was nominated for Outstanding Performance by a Male Actor in a Leading Role for his performance in A Star Is Born, which he also directed.
Gaga's talent aside, Cooper said it was her as a person that drew him in.More news: US charges Huawei in technology theft, sanctions violations
A Star Is Born has also received many nominations.
Gaga, 32, who played a young singer in A Star Is Born, is now in the midst of a residency at the MGM Park Theater, where she started her run of shows in December.More news: Grizzlies will listen to offers for stars Marc Gasol, Mike Conley
Lady Gaga and Bradley Cooper teamed up for the first time on stage to sing the powerful track in Las Vegas at the weekend.
A Star Is Born tells the tragic love story of ME, played by Cooper, who helps Gaga's struggling artist Ally.
Seemingly reluctantly, the actor joined her onstage, following her to the piano before quipping that "Jackson Maine would never wear these", as he struggled with some in-ear monitors. The thing is, we should all be crying right now.More news: EU drafting appeal for Maduro to call elections: diplomats