Jones, who guided the Wallabies to the 2003 World Cup final before his acrimonious departure two years later, is reported to be on Rugby Australia's (RA) short-list of candidates.
Cheika has said he would quit if Australia failed to win the Sept. 20-Nov. 2 World Cup in Japan.
"I am happy in Europe," Jones told the Sydney Morning Herald.
"The Wallabies need a generational change in culture."
Australia, ranked sixth in the world, won only four of 13 tests in 2018, their worst season in decades.
Jones is contracted to England until 2021 but his deal features a break clause if the team flops in Japan.
Jones's comments come two weeks after New Zealander Dave Rennie said he was unlikely to take over the Australia job while contracted to Glasgow Warriors until 2020.
New Zealander Warren Gatland, the Wales and British and Irish Lions coach, has also been reported to be on RA's short-list.
Gatland is leaving Wales after the World Cup and has also been linked with taking over at defending champions New Zealand once Steve Hansen leaves the role after Japan.
(Writing by Ian Ransom; Editing by Peter Rutherford)
