The British soul star met Burke when they appeared together on the TV show Star For A Night and they have remained friends ever since.
Burke's mother Melissa Bell, formerly of '90s group Soul II Soul, said: "Alex still visits her at her home in Devon and Joss has jetted her out to New York and Barbados for holidays."
However, Bell insisted that her daughter wants to win the show on her own merit, saying: "Alex wants to prove she can get to the top by herself."
She added: "I know she'll win. Leona Lewis is hailed as the next Mariah Carey, but Alex is the next Whitney Houston."
Burke auditioned for The X Factor in 2005 but failed to make it through to the live shows.