The former UK judge is said to be linked to a spot on the judging panel after Mel B replaced her on America's Got Talent last week.
Osbourne is now in line to swap places and take Mel B's previous job on The X Factor Australia, according to The Daily Mail.
''Simon is really keen for Sharon to go to Australia and be a judge over there," a source said.
''Simon knows that Sharon can be TV dynamite, and while the UK doesn't look like it will happen, Simon is set on the idea of Sharon going to Australia - she's part of his gang.''
Sharon Osbourne has been rumoured to be making a comeback on the UK version in recent months.
She fuelled the rumours after being spotted with Cowell, Louis Walsh and Sinitta at the Arts Club in Mayfair, London earlier this month.
She quit America's Got Talent back in July after NBC's handling of son Jack Osbourne's multiple sclerosis diagnosis.