Their first LP took home Best Traditional Pop Vocal Album seven years ago.
In a lengthy statement on Instagram, Gaga gushed: "Thank you so much to the @RecordingAcademy for these 6 nominations for Love For Sale. I am stunned and shocked and beyond grateful. I don't know what to say. I just keep crying and am utterly speechless.
"This means so much to me, @itstonybennett, the Bennetts, my family, jazz music, and the great Cole Porter who wrote all these timeless classics. I'll never forget today and congratulating Tony on his 6 nominations."
On Tony's reaction, she continued: "I'll never forget that today he could track every word I was saying and understood the world was celebrating him and celebrating jazz – a genre that embodies the joy, abundance and imagination of Black music throughout history.
"Thank you to all the Grammy voters for recognizing me and Tony's dedication to jazz music and for also recognizing it in major categories where this music is often not nominated. (sic)"
The 'Born This Way' singer admitted there is no better feeling than the "love and partnership" they share - despite their 60-year age gap.
Gaga concluded: "This album happened because it was Tony's idea and I made him a promise that we would make it and we did.
"At 95 years old, he has more nominations than ever, I'm so honored to be his companion in music and his friend.
"Thank you to the public for loving us, we surely love each other, and you.
"Believe in love and partnership, even with 60 years between us, and Alzheimer's, there is nothing like the magic of music. I love you Tony, and the world loves you too. How could they not?"
