Cheika, who coached the Wallabies in 68 tests from 2014-19, met Waugh at a Sydney restaurant, Australian media reported.
Rugby Australia (RA) declined to comment on the meeting but Waugh said in a statement that the governing body had made a targeted shortlist and received a high level of interest from "quality candidates around the world".
Schmidt will end his reign as Wallabies coach in October after this year's Rugby Championship, dashing local hopes the highly-regarded New Zealander would stay on until the 2027 World Cup.
Cheika is currently coach of Leicester Tigers but will exit the English club at the end of the season.
The 57-year-old coached Australia to the 2015 World Cup final in England but left the post in acrimony after the Wallabies crashed out of the 2019 quarter-finals in Japan.
Cheika later took over as Argentina head coach and left the role after guiding the Pumas to the 2023 World Cup semi-finals.
RA hopes to confirm Schmidt's successor in the coming weeks.
Former Ireland fly-half Ronan O'Gara, the head coach of French club La Rochelle, has thrown his hat in the ring for the job, while Australian Super Rugby coaches Les Kiss, Dan McKellar and Stephen Larkham are all considered to be in the frame.
Queensland Reds coach Kiss said on Wednesday he had spoken with RA but declined to comment on whether he was interested in the role.
"It is open knowledge that RA have spoken to all the coaches in Australia," he told reporters.
The new Wallabies coach's first job will be preparing the squad for a season-ending northern hemisphere tour starting in Tokyo against Eddie Jones's Japan on Oct. 25.
Australia will then meet England at Twickenham on November 1 followed by tests against Italy, Ireland and France, RA confirmed on Wednesday.