The 'Bleeding Love' singer - who shot to fame after winning the music mogul's UK TV talent show 'The X Factor' in 2006 - admitted she has remained close to her mentor, but is still nervous about how he will react to her music.
Speaking about recording some new material, she said: "He didn't come to the studio but I'd play him songs down the phone. It's scary and you think, 'Please like it!'
"We've formed more of a bond and we can be honest with each other."
As well as Simon, Leona says she has lots of celebrity friends, in particular Beatles legend Sir Paul McCartney and his family.
She said: "I have a relationship with the McCartneys. I respect their values and their opinions about vegetarianism because I'm a vegetarian. They're really cool people."
However, despite her successes, the singer admits she still gets overwhelmed when she meets other celebrities.
She added: "I was star-struck when I met Samuel L Jackson and Daniel Day-Lewis at the Golden Globes. I was excited when I met Nelson Mandela, too. I performed at his birthday in 2008. I was really honoured."