The Stevenage singer admitted to Digital Spy that the press attention is "quite annoying".
She said: "Yeah it's quite annoying, especially because there is no proof and no evidence that me and Aleks have anything going on.
"People have just assumed because we're mates and the same age - it's madness, utter madness."
The reality show pair recently took to Twitter to joke about the rumours.
Meanwhile, Team Jessie's other members Vince Kidd, Toni Warne and Cassius Henry lauded the 'Price Tag' singer amid speculation over her future on the BBC singing contest.
The Voice UK continues tomorrow night (Saturday) at 6.30pm on BBC One.
Additional reporting by Daniel Sperling