The 26-year-old single mum wowed judges on the ITV show with a heart-rending rendition of Amy Winehouse's You Know I'm no good.
Rachel, from North West London, has been candid about her ealier life of drug addiction, crime and underage sex.
She has also been open about the heartache of having three of her five children taken into care.
A show insider revealed: "Rachel is brilliant - it looks as if she could go far on the show.
"She has got past the boot camp and the next stage will be the judges' houses, which we will film in a week's time.
"That's when the four judges pick their final three and those 12 go through to the live shows - so Rachel is in with a great shot of making it."
Rachel lives with her two youngest children - son Tishon, six and daughter Tashanee, four. her older sons and a daughter have been adopted.
She still has basic contact, sending Christmas and birthday cards as well as other family news.
Rachel's troubled past has included jail for crimes including attempted burglary. She has said: "I'm not trying to hide anything.
"I know I took drugs and I know I committed crimes. I'm really remorseful for that.
"I've come out the other end and want to have a second chance to make my life better for me and my kids."
She has been free of drugs for six years.