The 71-year-old singer and 79-year-old country star discussed their longtime friendship on Wednesday's episode of Today prior to performing at Rogers' final concert in Nashville.
"First of all, she's hard to look at for me," Rogers joked.
"I'm not his type," Parton said.
Parton and Rogers' close relationship contributed to such hits as "Islands in the Stream," "Love is Strange" and "Real Love," but the pair remained platonic.
"I'm a believer that tension is better if you keep it than if you satisfy it," Rogers explained. "And then secondly, she said no to me."
"Nah. You know what, we were almost like brother and sister," Parton said. "And it would almost be like incest. So we just never went there."
Parton joined Rogers Wednesday evening at Bridgestone Arena for his Nashville show. Billboard reported the pair performed "You Can't Make Old Friends" and "Islands in the Stream," with Parton also surprising Rogers with a version of "I Will Always Love You."
"I couldn't be any happier to be tagged with someone like Kenny," the singer said. "He's a wonderful man, a wonderful singer and a wonderful duet partner. My heart will always be with Kenny. We're still going to be buddies."
Rogers will complete his All In for the Gambler farewell tour before retiring from live shows after six decades of performing. He previously told Rolling Stone Country he is grateful for his and Parton's success.
"Neither of us take ourselves for granted, and we're both kind of astonished as to what's happened with our lives and careers," the star said. "We're both very appreciative of it."