The Brit Award-winning star, 21, has been friends with 19-year-old Alex – through to the final 24 of the competition – since they were children, according to The Sun.
They have reportedly been in constant contact this series and Joss has apparently been secretly coaching the aspiring singer.
The girls met on TV show Star For A Night when Alex was 12 and Joss has been to stay at her family home in London.
Alex’s mother Melissa Bell – who was the lead singer of 90s pop group Soul II Soul – told the newspaper: “Alex still visits her at her home in Devon and Joss has jetted her out to New York and Barbados for holidays.”
Melissa hopes their friendship will help her daughter win the show, but added: “Alex wants to prove she can get to the top by herself.”
Alex first appeared on The X Factor in 2005 but failed to make it to the live shows.
This year she is one of the final 24 contestants and is already a hotly-tipped favourite to win.
Melissa said: “I know she’ll win. Leona Lewis is hailed as the next Mariah Carey, but Alex is the next Whitney Houston.”
Find out if Alex makes the Final 12 X Factor contestants on Sunday night at 6.10pm on ITV1.