The 25-year-old singer replied to the former astronaut on Twitter after he asked if she would write a song about him and told Buzz, 89 - who along with Neil Armstrong was one of the first two people to land on the moon - that she would be happy to dedicate an album to him.
The exchange occurred after NASA, the National Aeronautics and Space Administration, tweeted Ariana about her new song 'NASA', saying: ''Hey @ArianaGrande, we saw 'NASA' trending this morning and thought it was about one of our new discoveries. But we realized that you might need some space.
''It's like you're the universe and we're N-A-S-A.''
Buzz then replied saying: ''Do you think I'll make it into one of @ArianaGrande songs too!?'' and a thrilled Ariana wrote: ''buzz ... u can have a whole album honestly.''
She added: ''honest to god ... someone come check on me.''
Ariana has just released her new album 'Thank U, Next' with 12 tracks and she also dropped a brand-new music video for 'Break Up With Your Girlfriend, I'm Bored' .
Meanwhile, Ariana recently revealed she pulled out of performing at the Grammy awards because her ''creativity and self expression was stifled'' by the producers.
The singer had been due to take to the stage at Los Angeles' Staples Centre to sing one of her tracks this weekend but it was reported earlier this week that she now won't even be in attendance at the event.
And Ariana broke her silence on the matter, claiming producers of the event refused to allow her to show her ''creativity'', despite her offering up ''three different songs'' that she could perform.
Posting pictures from an article which included an interview with Grammys producer Ken Ehrlich in which he claimed Ariana couldn't ''pull something together'' in enough time, the '7 Rings' hitmaker wrote on Twitter: ''mhmmm here it is ! 'too late for her to pull something together......
''i've kept my mouth shut but now you're lying about me. i can pull together a performance over night and you know that, Ken. it was when my creativity & self expression was stifled by you, that i decided not to attend. i hope the show is exactly what you want it to be and more.
''i offered 3 different songs. it's about collaboration. it's about feeling supported. it's about art and honesty. not politics. not doing favors or playing games. it's just a game y'all.. and i'm sorry but that's not what music is to me. (sic)''
Ariana is nominated for two awards at the prestigious music event - Best Pop Vocal Performance for 'God Is a Woman' and Best Pop Vocal Album for 'Sweetener'.
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