The TV judge, who was on the panel from 2004 to 2007, met with Simon Cowell's representatives two weeks ago to discuss rejoining the show, The People reports.
> Simon Cowell wants original judges to return to 'X Factor'?
It is thought Osbourne is on board with making a comeback and will replace Tulisa Contostavlos.
"Sharon has been approached and discussions have begun about her returning for the 2013 show, she is really up for it," a source said.
"It is still early days in terms of contracts, but a return for Sharon is certainly the way things are looking at the moment.
"She was in the UK last month and X Factor bosses took the opportunity to put the idea to her. She had a long meeting with them and she has decided that she would love to come back.
"Louis [Walsh] can't contain his excitement, he has been begging Sharon to come back for years so he is desperately hoping it all works out."
Meanwhile, Contostavlos has apparently become "increasingly frustrated" about rumours that she will be axed from The X Factor.
An insider said: "Tulisa is over it, she has had enough of the politics on the show and doesn't want to go back.
"She is getting worried about how she is perceived on the show and thinks it would be better to quit while she is ahead to carry on with her music."
The report adds that Cowell wants Nicole Scherzinger to return in 2013 following her successful stint on The X Factor this year.
Photo gallery - The X Factor 2012 final - Jahmene vs James: