Reuters reports Australian Jones, who led the Wallabies to the 2003 World Cup final, has been linked with various roles at Rugby Australia since he was sacked by England in December.
"It's not going to happen," New Zealander Rennie told reporters, later adding: "It's not going to happen before the World Cup.
"We've had no discussions around changes to the coaching group ... what happens beyond 2023 is another matter."
Jones was equally blunt in an interview with the Guardian on Friday when he was asked whether he would be interested in working under Rennie.
"I'm not an assistant coach, mate," he told the newspaper. "I'm not interested in that sort of job."