The music mogul recently claimed he would have all his acts perform when he weds girlfriend Lauren Silverman and his 'X Factor' protégée - who shot to fame in 2006 with Simon's guidance - believes he would make her sing the hit ballad, which she recorded in 2009.
Leona told BANG Showbiz: "He'd probably get me to sing 'Happy' because I think that's one of his favourites of my songs."
The track is about taking chances no matter the potential risk, with lyrics including: "I gotta find my place, I wanna hear my sound, don't care about all the pain in front of me, 'cause I'm just trying to be happy."
Simon, 54, is expecting his first child - a boy - with Lauren and Leona, 28, admits it's "weird" to think of her close pal becoming a father.
She added: "It's so weird. I never thought I'd see the day but I think it's amazing. It's so lovely having a baby. I'm so happy for him."
Fatherhood won't stop the music executive from being heavily involved in Leona's career, however, as she insists he works very closely with her on her music.
She explained: "Simon's still the head of my label, still my A&R man ... so all my music, I send to him and we'll kind of sit down and listen to things together and go through it and see what we're feeling, what we're not feeling. So he's still very much involved in it."
Leona's album 'Christmas, with Love' is out now.