The 26-year-old singer/songwriter has revealed she asked their former record label Syco if she could pen some tracks for the chart-topping girl group - which is comprised of Jesy Nelson, Perrie Edwards, Leigh-Anne Pinnock and Jade Thirlwall - and, despite being turned down, she has vowed to "keep pestering" their team.
Speaking to The Sun newspaper's Bizarre column, Gabrielle said: “I would love to write a Little Mix record. They’re the coolest. That would be my dream. I went into (their former record label) Syco and begged to write for them but it never happened. Hopefully one day. I will keep pestering.”
The 'Home' singer is certainly dedicated to achieving her dreams, and recently joked that she will "retire" once she gets to meet Taylor Swift.
Gabrielle's song 'Miss You' was added to the 'Shake It Off' hitmaker's 'Songs Taylor Swift Loves' Spotify playlist in 2017, and the British star is still yet to meet her famous fan, but she is determined to make it happen.
The singer shot to fame in 2012, when her cover of Frankie Goes To Hollywood's 'Power of Love' for the John Lewis Christmas advert went to number one, but she was rejected by the supermarket chain before eventually landing the gig, and she is not one to take no for an answer.
Asked if she has bumped into the pop superstar yet, Gabrielle recently told BANG Showbiz: "No! I am dreaming about it. You know when you put something out in the universe and hope it happens...
"I did that for the John Lewis Christmas advert, they told me no, and I was like, 'I don't care, I am going to get this.'
"So I decided I was going to do it and go on tour in Brazil.
"So I have to, I've just got to try my best to make that happen."
She laughed: "Then I'll retire."