Cheika, who guided the Wallabies to the 2015 World Cup final, has already said he would walk away from the role if they do not go one better and win the Webb Ellis trophy in Yokohama next November.
While RA have not started preparing for that possibility yet, high performance manager Ben Whitaker said Jones, who coached the Wallabies from 2001-05, would be on any list he was instructed to draw up as a contingency.
"I can't speak on behalf of the board, but if I'm tasked with pulling together a list of potential candidates, is Eddie Jones on there, yeah he is," Whitaker told Australia's Fox Sports. "Quite obviously.
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"Where that goes in terms of the process that we run, well, that will be determined."
Whitaker said Jones' record as coach of England, they have won 24 of their 26 games since he succeeded Stuart Lancaster following their pool stage exit at the 2015 World Cup, simply put him in the conversation.
"You appreciate the skills he's got as a head coach," Whitaker said. "And if he's willing and able -- things you'd have to work out -- he'd be on the list, probably another dozen would be too."
Securing the 58-year-old's signature for a return home, however, would require a number of factors to fall into place.
Jones recently signed a contract extension with the Rugby Football Union until 2021, which involves him mentoring his successor for a year before he steps down.
The contract, however, includes a break clause based on England's performance in Japan.
He has also been mooted as a possible British and Irish Lions coach for their 2021 tour of South Africa, which could require a sabbatical from his England duties, something the RFU said they would allow.
(Writing by Greg Stutchbury in Wellington; Editing by John O'Brien)
