Aniston will give her first interview since boyfriend Justin Theroux proposed in August when she appears on Chelsea Lately tonight (October 15).
However, Handler - who is good friends with Aniston - told E! Online that she won't "focus on the ring".
"We don't want to be gross," she joked. "This isn't an ad for Zales - which I'm sure is where Justin bought it."
Handler also revealed that she does not expect any of the presidential or vice-presidential candidates to appear on Chelsea Lately, saying that President Barack Obama will not come on the show because she is "too decisive".
She added: "I'm not interested in [Republican candidates] Paul Ryan or Mitt Romney. I think they're both boring."
Aniston's interview with Handler will air on tonight's episode of Chelsea Lately, which begins on E! at 11pm ET.