O'Connor, who played the last of his 44 tests six years ago against Argentina, would join the Reds in the 2020 season on a minimum three-year deal, local broadcaster Fox Sports reported.
The Reds did not provide immediate comment when contacted by Reuters.
O'Connor made his Wallabies debut as an 18-year-old against Italy in 2008 but his international career was cut short in 2013 after a string of off-field incidents.
The Gold Coast-born 28-year-old last featured in Australian rugby in 2015 when he returned to the Reds in a bid to be selected for the World Cup in England and Wales that year.
But after a season blighted by injury and poor form, O'Connor was overlooked for the Wallabies squad and headed back to Europe.
While at Toulon in 2017, O'Connor was arrested for cocaine possession during a night out in Paris with former All Black Ali Williams and the French side declined to extend his contract.
He has stayed out of trouble since joining English club Sale Sharks later that year, and the sacking of fullback Israel Folau has left Cheika with a vacancy in his Wallabies backline.
Former Wallabies team mate Will Genia welcomed the prospect of O'Connor returning to Australian rugby, despite his record of indiscipline off the field.
"What people tend to do is typecast him as the arrogant kid who did this and that and judgement is clouded on who he might be now as a person," Genia told local media.
"While he was young he got away with a lot because of pure talent but at the point where he was judged disruptive to the team, it was decided he was not wanted.
"If the research is done and he has matured, as the indications are, why wouldn't you bring back someone as good as he is, whether it's into the Reds or the Wallabies set-up?"
(Reporting by Ian Ransom; Editing by Peter Rutherford)
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