Osbourne, who appeared on the show's first four series, tweeted her fans after the series nine launch on Saturday.
Responding to comments calling for her to come back to the ITV1 show, she wrote: "To everyone who tweeted about @TheXFactor tonight, thank you - I miss you too!
"Tell Simon [Cowell] to take me back for season 10. #XFactor "
Osbourne left the show in 2008 after a year of controversy surrounding her relationship with co-star Dannii Minogue. The pair have frequently spoken out in the press about their dislike for each other.
Ratings for series nine of The X Factor started off slow at the weekend, charting the show's lowest launch figures since series three.
Osbourne last appeared on the show in 2010, when she helped Louis Walsh at Judges' Houses and helped him pick acts including Wagner Carrilho and 'Tesco' Mary Byrne.
The X Factor continues on Saturdays at 8pm on ITV1.