The musician made the revelation on BBC Radio 6 Music, in an interview with presenter Shaun Keaveny.
Yorke was asked whether he would choose to go on Strictly or I’m a Celebrity... Get Me Out of Here! if he absolutely had to appear in one of these two programmes.
“Oh Strictly,” he promptly responded. “I think they asked me once.”
He said the offer came during the early days of the programme and left him somewhat bewildered.
“I was like, ‘You what?’” he added. ”I’m pretty sure I got the call from the office one day.”
Strictly‘s 17th series premiered on 7 September.
Support free-thinking journalism and attend Independent events
Made In Chelsea star Jamie Laing was forced to drop out of the programme ahead of its launch after tearing a ligament in his foot.
Emmerdale‘s Kelvin Fletcher has stepped in to replace him.