Sex offender Edwards, 63, discusses the dance show invitation during a chat with Radio 2 legend Steve Wright, first broadcast in January 2019.
During the interview, the ex-newsreader, who quit the BBC during a police probe into child abuse images, is described as a "beloved man of the people".
The interview, on Steve Wright's Big Guests podcast, was taken off BBC Sounds after the Daily Express flagged up its content in light of Edwards' conviction.
During the chat with Wright, who died in February aged 69, Edwards had said he would ponder the Strictly offer over the summer. In the end he did not appear on the series.
Shamed
On being squeezed into tight-fitting costumes for the show, he said: "That's what really scares me, actually."
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