"He didn't get on a knee, thank God," Grande told Sang. "No, that would've been so googly."
A fan in the "Sweetener Slumber Party" audience piped up and said that he had read details about Davidson's proposal. "What did you hear? What that he was high?" Grande asked, laughing. "He's always high!"
The pop star explained that she never really thought that she would get married until the "SNL" star came along.
"I'm not like a very traditional person so the fact that I'm getting married is something I never even saw coming," Grande said. "I never saw that coming, I never wanted that."
"I was like, 'F--k that, there's no point,' like what's the point?" she added "Then I kind of understood it once I found the right person."
Grande shared the story about how she and Davidson met on "Saturday Night Live" when she hosting the show. Ariana -- a huge Harry Potter fan -- was immediately smitten after catching a glimpse of his Deathly Hallows tattoo.
"I remember when I was rehearsing my monologue, I like looked off stage right where he was like waiting to come on and be like, 'Hey do you wanna smoke some pot?'" she recalled, showing off her spot-on impression of her fiancé. "And I like saw that he had his sleeve...and I saw the f--king Deathly Hallows here and the tiny tip of a Dumbledore quote."
Grande added that since she thought he was "cute" and was looking over, she approached him about his ink. "I was like, 'Is that the Deathly Hallows?!' and he was like, 'Yeah!' and I was like 'carry on' and I walked away and that was really it."
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"I left his writers' room where we were writing skits and stuff for the show," Grande told Fallon. "And I jokingly said to my tour manager, 'I'm marrying him, 100 percent.' I was like, 'I'm literally gonna marry him.'"
Even better? "We weren't even friends, didn't even see him at the after-party," Grande admitted. In fact, she said they weren't friends "for a long time" after that.
"I had the biggest crush in the world on him the whole time, like forever," she added. "Like my friends used to make fun of me and all that stuff."