Jessie also said she hoped to work with her own act Matt Henry, but didn't mention the show's winner, Andrea Begley.
Speaking ahead of the release of her new Wild EP, Jessie told the DigitalSpy website: "I'm so hard on myself that when I'm in the studio, I'll write 10 songs and only use one. So those nine songs that are left over, I always think where could these go? Who could they be for?
"I'd love to actually write with Leah [McFall] and Matt [Henry] from The Voice, which I'm really excited about."
Leah and Matt both finished as runners up on last month's final, but Leah confessed she almost didn't enter the BBC One show.
She admitted this week: "I got quite nervous about it - I wasn't quite sure how I would come across on TV.
"And I was apprehensive about whether or not people would like my voice because I know it's like Marmite and I don't even like Marmite!"
Despite not winning, Leah's hopeful of a bright future with the help of her coach Will.i.am.
She added: "Seeing how incredibly talented Will is and seeing what vision he has, I'd love ot work with him again. That's looking likely, which would be amazing."