The 59-year-old, who initially left amid rumours of fights with fellow panellist Dannii Minogue, told the Daily Star Sunday that she would jump at the chance to rejoin the show.
"I would love to come back to X Factor," she said. "I want to come back to England and I want to come back to X Factor. I'm not happy to be back, I am ecstatic to be back."
Osbourne recently quit her role on America's Got Talent and had previously ruled out a return to The X Factor after feuding with Simon Cowell. However, she has now revealed that Cowell offered her support following her son Jack's recent multiple sclerosis diagnosis.
"Simon and I are still in touch," she said. "He reached out to me very recently regarding Jack and he was so lovely and so supportive.
"When the s**t hits the fan, Simon is always there for you. We bicker like brother and sister but ultimately we have got each other's backs.
"I would love to work with Simon again just to p*ss him off."
Osbourne initially sparked rumours of her return to the ITV talent show last month when she tweeted "Tell Simon to take me back for season 10" to her 1.2m followers.
However, the outspoken music manager will first make a short-lived return to screens during the current series of the show, where she will be seen assisting Louis Walsh at the Judges' Houses stage of the competition.
"The magic that comes from the two of us rubbing together, it's electric," she said, talking about her on-screen chemistry with Walsh.
"It's like riding a bike, you never forget. We could cause lightning because we are like lightning in a bottle."
She added: "I am looking for an act that can take Louis to the winning place of The X Factor this year.
"Louis has to win this year and we are going to find him the act that will take him all the way."
Walsh also praised Osbourne's temporary return to the show, declaring: "The bitch is back."
"She is just honest," he explained. "She is a self-made person and she just speaks her mind. She is more experienced than anyone else [on the panel, and] there is nothing this woman hasn't done or said.
"She is just different. She is a bit mad but in a good way and that's great."